I am trying to solve the following equation using Laplace method
ty" + (4t-2)y' - 4y = 0; y(0)=1 and y'(0)=constant
I have not come across a problem in this form (specifically the 4t-2), thus I am confused as to how I should begin the problem. Any pointers leading me in the correct direction would be much appreciated.
Multiplication by t corresponds to the negative derivative in the s domain. See here. So it looks to me as though the LT is going to reduce the order of your DE by one, instead of reducing it to an algebraic equation altogether.