General solution of differential equation system

[mansfin]

Homework Statement

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

Homework Equations

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&#039;}{12}=\frac{5}{2}Ae^{-20t} \rightarrow y(0)=B<br /> 0=\frac{5}{2}A<br /> A=0<br /> <br /> 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!

 

[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.