Differential Equations LaPlace tranform method

Use the LaPlace transform method to solve the initial value problem y'''+y''-2y'+y=cos2t, y(0)=1, y'(0)=0, y''(0)=-1 Please show all work! Thanks

General solution to a 2nd + 4th order DE

a) y'''' - 11y''' +45y"-81y'+54y = (t+1)e^(3t) find general solution to both the above and below b) y''+y=tcost

3rd order DE using Variation of Parameters

y"'+4y' = cot 2t variation of parameters to solve above equation.

elimination method 1

The following problem (attached) needs to be solved using the elimination method.

Second Order

Find general solution of a second order differential equation.