Pls answer two parts it is part of one question. I need asap

a) Prove that if f(t+)= -f(t), then

L{f(t)}= e^-st f(t)dt/1+e^-s

b) The Laplace transform L{e^-t^2} exists (because it is of exponential order), but without finding it solve the initial-value problem

y''+y=e^-t^2, y(0)=0, y'(0)=0

Your final answer may contain anintegral form.