Solve IVP DE: x'=-3x+4y-2, y'=-2x+3y, x(o)=-1, y(o)=3

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Thanks for the help.

Homework Statement



Solve the IVP: x'=-3x+4y-2, y'=-2x+3y, x(o)=-1, y(o)=3


The Attempt at a Solution


x''=-3x'+4y'
x''=-3x+4(-2x+3y)=-3x-8x+12y
y=(x'+3x+2)/4
x''=-3x-8x+12((x'+3x+2)/4)
x''-x=6
xgeneral=xh+xp
Xg=Ce^t+Ce^-t-6
Yg=1/4(Ce^t-Ce^-t+3Ce^t+3Ce^t)
Yg=Ce^t+1/2(Ce^-t)-4
x(t)=
y(t)=
 
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Discussion

there's an error in your first line, where you've replaced x' with x

why not write in matrix form and solve as a system of linear equations