Solve second order differential equation by Laplace transform

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.

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Originally Posted by cheme

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.

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Take the Laplace transform of each term. Where are you stuck in doing this? Note that (4t-2)y' can be re-written as 4ty' - 2y' ....

Yes, but I am unsure what to do with a variable in front of the differentials.

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.