using the Laplace transform solve the IVP
y'' +4y= 3sin(t) y(0) =1 , y'(0) = - 1 , i am stuck on the
partial fraction decomposition step. please explain the
decomposition clearly.
Solve using the Laplace transform: y" + 4y = g(t) where y(0) =
y'(0).
Hint: Use the convolution theorem to write your answer. You may
leave your answer expressed in terms of an integral.
Take the Laplace transform of the following initial value and
solve for Y(s)=L{y(t)}: y′′+4y={sin(πt) ,0, 0≤t<11≤t
y(0)=0,y′(0)=0
Y(s)= ? Hint: write the right hand side in
terms of the Heaviside function. Now find the inverse transform to
find y(t). Use step(t-c) for the Heaviside function u(t−c) .
y(t)= ?