One issue computer investigators face is that normal file utilities can irrevocably change files, effectively "polluting" the crime scene as well as deleting evidence you need. For example, viewing files with a regular editor changes things like the timestamp. Imagine someone tromping through a real crime scene in dirty boots and moving objects all over the house. This is the same as rummaging through your system without the proper tools. Not only will you have eliminated your chance of being able to take any criminal or civil action, but you may also erase the attacker's digital trail. Hackers often use tools that hide processes and files from normal system utilities, so you need special tools that operate outside of the normal operating system to look beyond what the operating system thinks it sees.

The following sections review tools for both Linux and Windows. First we will look at a few of the investigation tools on operating systems, then at full-featured toolkits for deeper analysis. Keep in mind that using operating system-based tools may return false or bogus data if your OS has truly been compromised.

This little system add-on can be useful when investigating a machine for suspicious activity. Often a memory-resident virus or Trojan horse will show up as a process running under a strange name or on an unusual port. Fport looks for open TCP or UDP network ports and prints them out along with the associated process id (PID), process name, and path. It is similar to the native Windows netstat command except that it provides a little more information and allows you to format it different ways for analysis. This can help you track down suspicious programs that are opening up network ports on your machine. This behavior is the hallmark of a Trojan horse.

Of course, every process you don't recognize isn't necessarily an evil program, but you should understand what weird-looking services are doing. The most obvious ones will have nonstandard paths (other than the Windows system directories and such). Also, strange or hacker-like names are a dead giveaway.

The program is designed and offered by Foundstone Corporation, a security software and consulting company. They offer several other free security tools and their Web site is worth a look. While Fport is not purely open source (only the binaries are distributed), it is freeware and there are few limitations on its use for commercial purposes.

Installing Fport

Download the zip file from the Foundstone Web site and unzip it into its own directory. There will be two files, the Fport executable and a short README file.

Using Fport

Fport can help you figure out if a machine has been tampered with and where the intruder is coming from. You need to run Fport on a system that is live, that is, up and running; you can't run Fport on static data.

Running Fport is about as simple as it comes. From the directory the executable is in, type fport. It prints a listing of all the ports open at that moment and their associated applications (see Listing 11.1).

Listing 11.1. Fport Display

By looking at this listing, you can see what appear to be normal services and programs running, until about half way down where you can see that cmd.exe is running from the temp directory. This is the command prompt binary and it has no business being in a temp directory. Also, the fact that the service has no name should arouse suspicion. Finally, the incoming port number doesn't match any known services. In fact, if you look it up in a database of known Trojan horses on the Internet (www.simovits.com/trojans/trojans.html) , it matches the port number of a documented Trojan horse. There is strong evidence that this system has been exploited. At this point, you have to decide if it is worth taking the system down to do further forensic analysis of the system.

Table 11.1 lists a few options you can run with Fport to sort the output. You can also use the –h option to display short help descriptions.

If you have a lot of processes, you can use these switches to look at all the high port numbers running, which is typically where malware runs. You can also sort by application path or name to find nonstandard applications running.

This tool is similar to the Fport tool for Windows just discussed. The lsof tool (LiSt Open Files) associates open files with processes and users. It is like the netstat command, but in addition it reports the network port the service is using. This is important when trying to track down an active program on the network. Often the only way to find these elusive bugs is to watch for what network ports they open up.

The lsof tool is being preinstalled on some UNIX and Linux distributions and is available in RPM form on the installation disks of others such as Mandrake and RedHat Linux. To see if you have it preinstalled, type lsof and see if you get any response.

Installing lsof

Solution Manual Of Differential Equation By Bd Sharma: New!

Don't just copy the steps. Understand the why . Once you do, solving differential equations transforms from a chore into a puzzleâ€”and a satisfying one at that.

The search for the phrase "solution manual of differential equation by bd sharma" yields a specific result: a document listed as Differential Equations [solution Manual] hosted on the vdoc.pub website. Here are the key details:

The manual typically follows the chapter structure of the main textbook, providing comprehensive solutions to exercises.

An official, standalone solution manual published directly by Dr. B.D. Sharma or Krishna Prakashan is not widely available in commercial bookstores. However, students can access step-by-step solutions through several alternative avenues: 1. Compiled Student Editions and Key Books

Websites like ResearchGate, Academia.edu, and Scribd often host PDFs uploaded by senior students or research scholars containing handwritten or typed solutions to specific chapters of B.D. Sharma. Online Educational Communities solution manual of differential equation by bd sharma

A guide on the official solution manual?

It is crucial to clarify that . The widespread use of RD Sharma's textbooks for secondary school mathematics (Classes 11 and 12) often leads to this confusion. When searching for "BD Sharma solution manual," most general educational websites (e.g., Vedantu, Careers360) will return results for RD Sharma's Differential Equations chapter (Chapter 22). The table below highlights the key differences to help students select the correct resource:

Solution manuals are an essential resource for students and researchers working with differential equations. They provide:

Relying solely on a solution manual can hinder your learning. Use these strategies to maximize your academic performance: Don't just copy the steps

Unlike the main textbook, which contains only the questions, the solution manual provides to every exercise. B.D. Sharmaâ€™s book is famous for its massive collection of problemsâ€”ranging from simple variable-separable forms to complex Partial Differential Equations (PDEs). The manual bridges the gap between "I think I know this" and "I can prove it."

2. Differential Equations of the First Order but Not of the First Degree Equations solvable for Equations solvable for and equations solvable for Clairautâ€™s equation and singular solutions. 3. Linear Differential Equations with Constant Coefficients Finding the Complementary Function (C.F.).

by Dr. B.D. Sharma is a foundational textbook widely utilized in undergraduate engineering and mathematics programs across Indian and South Asian universities. The book is noted for its structured approach, moving from fundamental definitions to complex applications in mathematical physics and engineering. Key Topics Covered

To ensure that a solution manual enhances your learning rather than making you dependent, adopt the following study habits: The search for the phrase "solution manual of

: Dr. Sharma includes over 1,600 examples and university exam questions within the text. Many students find these model solutions sufficient to solve the end-of-chapter exercises.

Differential equations have numerous applications in various fields, including:

The book is meticulously structured to align with the UGC curriculum for undergraduate courses on differential equations offered by all Indian universities. Below is a detailed table of contents, compiled from a 2017 edition, which illustrates the comprehensive scope of the book.

Never look at the solution until you have struggled with a problem for at least 20 minutes.

| Part | Chapter | Main Sections | | :--- | :--- | :--- | | | I. INTRODUCTION | Basic definitions, classifications | | | II. EQUATIONS OF FIRST ORDER AND FIRST DEGREE | Variable separable, Homogeneous equations, Linear equations, Bernoulli's equation, Problems of curves | | | III. EQUATIONS OF FIRST ORDER AND FIRST DEGREE [CONT.] | Exact differential equations, Integrating factors | | | IV. TRAJECTORIES | Orthogonal and self-orthogonal trajectories | | | V. LINEAR DIFFERENTIAL EQUATION WITH CONSTANT COEFFICIENTS | Auxiliary equation, Particular integrals, Exceptional cases | | | VI. HOMOGENEOUS LINEAR EQUATION | Equations reducible to homogeneous form | | | VII. EQUATIONS OF THE FIRST ORDER BUT NOT OF THE FIRST DEGREE | Equations solvable for p , y , x , Clairaut's equation | | | VIII. SINGULAR SOLUTIONS | Tac-locus, nodal locus, cusp locus | | II | I. EXACT DIFFERENTIAL EQUATIONS AND EQUATIONS OF PARTICULAR FORMS | Dependent variable absent, Equations in which x is absent, Condition of exactness, Integrating factor, Nonlinear equations | | | II. LINEAR EQUATIONS OF SECOND DEGREE | One integral of C.F. known, Removal of first derivative (Normal form), Changing the independent variable, Method of variation of parameters, Method of operational factors | | | III. SIMULTANEOUS DIFFERENTIAL EQUATIONS | Different methods, Number of arbitrary constants, Method of solving dx/P = dy/Q = dz/R , Geometrical interpretations | | | IV. TOTAL DIFFERENTIAL EQUATIONS | Conditions for integrability, Methods of solution |

Application of Laplace transforms to solve differential equations.

Using lsof

The lsof program has many uses, and has extensive man pages and several README files for the different applications. However, this section concentrates only on a few specific commands that are useful for forensic research.

If you want to see all of the open files on your system at any given moment and the processes associated with them, type:

The -n option tells lsof not to attempt to do a DNS record on any IP addresses connecting to your machine. This speeds up the process considerably. The output will look something like Listing 11.2

Listing 11.2. lsof –n output

The connections in this listing look normal. The connection via the rwho service might give you pause. You would want to make sure that a valid user on your system is using this command legitimately. If this account belonged to a nontechnical secretary type, you might want to investigate this further.

You can also use lsof to look for a specific file. If you want to see if anyone was accessing your password file, you could use the following command:

Replace path/filename with the specific path and filename you are interested in, in this case, /etc/passwd. You have to give lsof the whole path for it to find the file.

Another way to use lsof is to have it list all the open socket files. This shows if there is a server listening that you don't know about. The format of this command is:

This produces output similar to Listing 11.3. You can see all the programs you are running, including sshd and nessusd, which are the daemons for Nessus and SSH. You can even see the individual connections to these services. It looks like someone is using the Nessus server at the moment. Checking the IP address, you can see that it is an internal user. In fact, it is your own machine! So there is nothing to worry about this time.

Listing 11.3. lsof –i Output

You can specify a particular IP address or host to look for by putting an @ (at sign) and the address after the -i switch. For example:

shows any connections coming from within your network, assuming your internal network is 192.168.1.0/24.

Forensic Analysis Tools

Fport: A Process Identification Tool for Windows