Question

Find the solution of y'' + 4y = 3t. y(0)=0, y'(0)=0

Answer 1

r^2 + 4 = 0
r = 2i, -2i

Answer 2

\[Y _{h}=c _{1}\sin2t + c _{2}\cos2t\]

Answer 3

Thats where I am

Answer 4

I know I need Yp and use that to find all the constants. I need help setting up Yp

Answer 5

your right hand side is a linear polynomial so u choose ypur \(Y_p\) like this:
\[Y_p=At+B\]

Answer 6

say my right side was t^2 +2t would it be At^2 + 2B +C ?

Answer 7

plug in the original equation and find A ,B

Answer 8

yes thats right

Answer 9

B2t

Answer 10

Ok I can do the rest, thx @mukushla

Answer 11

no problem