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System of ODEs

The problem goes like this:

"Show that [itex]x = \sin(2t) + e^t, y = 2\cos(2t) - 4e^t[/itex] is a solution of
[tex]x' = 5e^t + y, y' = -4x [/tex]
and find a family of solutions of this system.

I already did the 'showing' part. I am having trouble finding the general solution for this system. Can someone help me?
 

OlderDan

Science Advisor
Homework Helper
3,021
1
Have you looked at the second derivative of x?
 

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