What is the solution for y^{''}-y^'-2y=-4t+6t^2 ?

The solution for y^{''}-y^'-2y=-4t+6t^2 is y=c_{1}e^{2t}+c_{2}e^{-t}-3t^2+5t-11/2

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y^{''}-y^'-2y=-4t+6t^2

y^{^{''}} - y^{^{'}} - 2 y = - 4 t + 6 t^{2}

y = c_{1} e^{2 t} + c_{2} e^{- t} - 3 t^{2} + 5 t - \frac{11}{2}

Solution steps

y^{''} (t) - y^{'} (t) - 2 y = - 4 t + 6 t^{2}

Solve linear ODE:

y = c_{1} e^{2 t} + c_{2} e^{- t} - 3 t^{2} + 5 t - \frac{11}{2}

y = c_{1} e^{2 t} + c_{2} e^{- t} - 3 t^{2} + 5 t - \frac{11}{2}

\int x e^{6} d x

f (x) = - 2 x + 3

\int (x \cdot cos (x)) d x

\int x^{2} sec^{2} (x^{3} + 1) d x

What is the solution for y^{''}-y^'-2y=-4t+6t^2 ?
The solution for y^{''}-y^'-2y=-4t+6t^2 is y=c_{1}e^{2t}+c_{2}e^{-t}-3t^2+5t-11/2