How to go about this question solving differential equations

Thread starter sozener1
Start date Sep 27, 2014
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Differential Differential equations

In summary, differential equations are mathematical equations used to model real-world phenomena in fields such as physics, engineering, and economics. The process for solving them involves identifying the type of equation, using integration and other techniques to find a general solution, and then applying initial or boundary conditions. Differential equations can be solved analytically or numerically, and there are various software and tools available for this purpose. To improve skills in solving differential equations, a strong foundation in calculus and algebra, practice, and familiarizing oneself with solution techniques and resources are recommended.

Sep 27, 2014

sozener1

from the attachment

a) when I put dw/dt = 0 I get something like e^(b/a) is this correct?

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Sep 27, 2014

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sozener1 said:

from the attachment

a) when I put dw/dt = 0 I get something like e^(b/a) is this correct?

Do not post thumbnails; they are unreadable on some media. Just type out the problem. (See the 'pinned' post 'Guidelines for students and helpers', by Vela, which explains the reasons behind this standard.)

FAQ: How to go about this question solving differential equations

1. What are differential equations and why do we need to solve them?

Differential equations are mathematical equations that describe the relationship between a function and its derivatives. They are used to model real-world phenomena in fields such as physics, engineering, and economics. By solving differential equations, we can understand how a system changes over time and make predictions about its behavior.

2. What is the process for solving a differential equation?

The process for solving a differential equation involves several steps. First, we must identify the type of differential equation (e.g. linear, separable, exact) and determine the appropriate method for solving it. Then, we use integration and other mathematical techniques to find a general solution. Finally, we can use initial or boundary conditions to find a particular solution that fits the given problem.

3. Can differential equations be solved analytically or numerically?

Yes, there are two main approaches to solving differential equations: analytical and numerical. Analytical solutions involve finding an exact algebraic expression for the solution, while numerical solutions use approximations and algorithms to find an approximate solution. Both approaches have their advantages and are used in different contexts.

4. Are there any software or tools available for solving differential equations?

Yes, there are many software and tools available for solving differential equations. Some popular options include MATLAB, Mathematica, and Maple. These programs use numerical methods to solve differential equations and can handle complex equations that may be difficult to solve analytically.

5. How can I improve my skills in solving differential equations?

To improve your skills in solving differential equations, it is important to have a strong foundation in calculus and algebra. Practice is also key, so try solving a variety of problems and challenge yourself with more complex equations. Additionally, familiarize yourself with various solution techniques and tools, and seek out resources such as textbooks, online tutorials, and workshops to deepen your understanding.