How does one evaluate the Laplace of functions like $t^2\frac{d^2y}{dt^2}$ ?
I wanted to solve a differential equation using Laplace Transform resembling: $x^2\frac{d^2y}{dx^2} + x\frac{dy}{dx} + y = 5$
MATLAB Provides me the answer as :
C6*cos(log(t)) + C5*sin(log(t)) + 5
Can someone give me a derivation for this?