# Homework Help: General solution of differential equation system

1. Oct 29, 2009

### mansfin

1. The problem statement, all variables and given/known data

Find the general solution of the system of differential equations
$$x'=10x - 12y$$
$$y'=25x - 30y$$
(where primes indicate derivatives with respect to t) by using the initial conditions
$$x(0)=A$$
$$y(0)=B$$

2. Relevant equations

3. The attempt at a solution

$$x''=10x' - 12y'$$
$$y'=25x-30y$$
$$x''=10x'-12(25x-30y)$$
$$y=\frac{10x-x'}{12}$$
$$x''=10x'-300x+360(\frac{10x-x'}{12})$$
$$x''=10x'-300x+300x-30x'$$
$$x''+20x'=0$$
$$r^2+20r=0$$
$$r(r+20)=0$$
$$r=0,-20$$
$$x(t)=Ae^{-20t} +B$$ $$\rightarrow$$ $$x(0)=A$$
$$A=A+B$$
$$B=0$$
$$y=\frac{10x-x'}{12}=\frac{5}{2}Ae^{-20t} \rightarrow [tex]y(0)=B$$
$$0=\frac{5}{2}A$$
$$A=0$$

If A=0 and B=0, then my general solutions x(t),y(t)=0. This is clearly not right. What am I doing wrong? Thanks!

2. Oct 29, 2009

### LCKurtz

Use C and D in your general solution so they don't get mixed up with the A and B in the initial conditions.