Find the general solution of

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- Apr 26th 2008, 10:15 AMmatty888Find general solution
Find the general solution of

http://www.cramster.com/Answer-Board...1272542368.gif - Apr 26th 2008, 10:18 AMMathstud28
- Apr 26th 2008, 10:34 AMflyingsquirrel
Hi

First, solve the homogeneous equation $\displaystyle \frac{\mathrm{d}^2y}{\mathrm{d}x^2} +4 \frac{\mathrm{d}y}{\mathrm{d}x} +3y=0$. It implies : writing the characteristic equation and finding its root. Then, using these roots, you can deduce an expression of the solution $\displaystyle y_h$.

Then, find a particular solution $\displaystyle y_p$ of $\displaystyle \frac{\mathrm{d}^2y}{\mathrm{d}x^2} +4 \frac{\mathrm{d}y}{\mathrm{d}x} +3y=2\exp(-3x)$. It can be achieved by showing that $\displaystyle y_p(x)=\lambda \exp(-3x)$ is a solution for some value of $\displaystyle \lambda$. (usually, if the second member is a polynomial of $\displaystyle \exp x$ searching for a particular solution of this form works well)

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