# Find general solution

• Apr 26th 2008, 10:15 AM
matty888
Find general solution
• Apr 26th 2008, 10:18 AM
Mathstud28
Quote:

Originally Posted by matty888

You are starting to annoy me...you have posted like 12 questions...didnt thank those who helped you..and most of all you havent even tried to answer it yourself...if you show some work I will help you
• Apr 26th 2008, 10:34 AM
flyingsquirrel
Hi

First, solve the homogeneous equation $\frac{\mathrm{d}^2y}{\mathrm{d}x^2} +4 \frac{\mathrm{d}y}{\mathrm{d}x} +3y=0$. It implies : writing the characteristic equation and finding its root. Then, using these roots, you can deduce an expression of the solution $y_h$.
Then, find a particular solution $y_p$ of $\frac{\mathrm{d}^2y}{\mathrm{d}x^2} +4 \frac{\mathrm{d}y}{\mathrm{d}x} +3y=2\exp(-3x)$. It can be achieved by showing that $y_p(x)=\lambda \exp(-3x)$ is a solution for some value of $\lambda$. (usually, if the second member is a polynomial of $\exp x$ searching for a particular solution of this form works well)

The solution of the complete equation will be the sum $y_h+y_p$.