I am having trouble with the below problem:(adsbygoogle = window.adsbygoogle || []).push({});

y'-(3/2)y= 3t+ 2e^t, y(0)= y0. fine value of y0 that separate solutions that grow positively and negatively as t=> infinity.

I found p(t) to be -3/2, u(t) to be e^-3t/2

=> e^-3t/2*y' - 3y/2( e^-3t/2)= e^-3t/2(3t+ 2e^t)

=> -2 -4e^t + ce^ 3t/2

where I found c = y0+6/ e

Do you guys see any errors in my math so far? i am confused as to find y0 where the solutions diverge (pos. vs neg)

Thanks

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# Homework Help: Initial Value problem

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