Question about simple diff eq question

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In summary, a simple differential equation is an equation that relates an unknown function to its derivatives. It can be solved using separation of variables, and differs from a partial differential equation which involves multiple independent variables. Multiple solutions are possible for a simple differential equation, and it has various real-life applications in fields such as science and engineering.
  • #1
bboy
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hi guys..i got a problem while doing my diff eq assignment:confused:
hope u guys can give me hand..any help ll be appriciated
Obtain the solution of the diff eq..

x' + ax = A sinωt
x(0)= b

thnx guys..
 
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  • #2
Is omega a constant, and x a function of t? If so then this can be solved with an integrating factor.
 

1. What is a simple differential equation?

A simple differential equation is an equation that relates an unknown function to its derivatives. It can be represented in the form: y' = f(x,y).

2. How do you solve a simple differential equation?

The most common method for solving a simple differential equation is by using separation of variables. This involves isolating the variables on opposite sides of the equation and integrating both sides to find the general solution.

3. What is the difference between an ordinary differential equation and a partial differential equation?

An ordinary differential equation involves a single independent variable, while a partial differential equation involves multiple independent variables. This means that the derivatives in a partial differential equation can be with respect to different variables, while in an ordinary differential equation they are all with respect to the same variable.

4. Can a simple differential equation have multiple solutions?

Yes, a simple differential equation can have multiple solutions. This is because the general solution of a simple differential equation usually includes a constant of integration, which can take on different values and result in different specific solutions.

5. What are some real-life applications of simple differential equations?

Simple differential equations are used in various fields of science and engineering, such as physics, chemistry, biology, and economics. They can be used to model and analyze various physical systems, such as population growth, chemical reactions, and circuit dynamics.

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