Question

Solve the IVP with Laplace transforms
\[2y''+3y'+5y = \sin 2t,\qquad y(0)=-1,\qquad y'(0)=1\]

Answer 1

Is there a nicer way?

Answer 2

try completing the square on RHS


\(\hat y (2((p+\frac{3}{4})^2 + \frac{31}{16})) = 1 - 2p + \mathcal{L} \{ \sin 2t \}\)


so you're straight into a sinusoid on the first 2 terms on LHS

and maybe a convolution for the final term

check algebra but completing the square is as a general rule the better way to go when it doesn't factor

horrible stuff!!!

Answer 3

oops got the LHS and RHS wrong way round....