Solve the given system of linear differential equations by systematic substitution. dx/dt+dy/dt=2x+2y+1 dx/dt+2dy/dt=y+3 Here's what I got for x and y:

y=c1e^(t)+c2e^(2t)-3
x=c3e^(t)+c4e^(2t)+5/2

But when I plug it back into the first equation I get: c3e^(t)+2c4e^(2t)+c1e^(t)+2c2e^(2t)=2x+2y+1

And I have no idea where to go from there.

Question

Solve the given system of linear differential equations by systematic substitution. dx/dt+dy/dt=2x+2y+1 dx/dt+2dy/dt=y+3 Here's what I got for x and y: 

y=c1e^(t)+c2e^(2t)-3 
x=c3e^(t)+c4e^(2t)+5/2 

But when I plug it back into the first equation I get: c3e^(t)+2c4e^(2t)+c1e^(t)+2c2e^(2t)=2x+2y+1 

And I have no idea where to go from there.

anonymous · Answer

My brain turned off for a minute. You just gotta plug in x and y.