1. ## Find general solution

Find the general solution of

2. Originally Posted by matty888
Find the general solution of
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

3. 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 $y_h+y_p$.