What is the solution for y^{''}-y^'-2y=4t^2,y(0)=1,y^'(0)=4 ?

The solution for y^{''}-y^'-2y=4t^2,y(0)=1,y^'(0)=4 is y=2e^{2t}+2e^{-t}-2t^2+2t-3

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y^{''}-y^'-2y=4t^2,y(0)=1,y^'(0)=4

y^{^{''}} - y^{^{'}} - 2 y = 4 t^{2}, y (0) = 1, y^{^{'}} (0) = 4

y = 2 e^{2 t} + 2 e^{- t} - 2 t^{2} + 2 t - 3

Solution steps

y^{''} (t) - y^{'} (t) - 2 y = 4 t^{2}

Solve linear ODE:

y = 2 e^{2 t} + 2 e^{- t} - 2 t^{2} + 2 t - 3

y = 2 e^{2 t} + 2 e^{- t} - 2 t^{2} + 2 t - 3

What is the solution for y^{''}-y^'-2y=4t^2,y(0)=1,y^'(0)=4 ?
The solution for y^{''}-y^'-2y=4t^2,y(0)=1,y^'(0)=4 is y=2e^{2t}+2e^{-t}-2t^2+2t-3