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

The solution for y^{''}-y^'-2y=-6t+4t^2 is y=c_{1}e^{2t}+c_{2}e^{-t}-2t^2+5t-9/2

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

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

y = c_{1} e^{2 t} + c_{2} e^{- t} - 2 t^{2} + 5 t - \frac{9}{2}

Solution steps

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

Solve linear ODE:

y = c_{1} e^{2 t} + c_{2} e^{- t} - 2 t^{2} + 5 t - \frac{9}{2}

y = c_{1} e^{2 t} + c_{2} e^{- t} - 2 t^{2} + 5 t - \frac{9}{2}

\int_{- 2}^{4} ∣ - 2 x + 4 ∣ d x

y^{^{'}} - \frac{2}{x} y = 0

\frac{\partial}{\partial x} (\frac{7 x ^{2}}{( x - y ) ^{2}})

\int_{1}^{t} \frac{3}{x ^{3}} d x

\int \frac{1}{9 x ^{2} + 4} d x

What is the solution for y^{''}-y^'-2y=-6t+4t^2 ?
The solution for y^{''}-y^'-2y=-6t+4t^2 is y=c_{1}e^{2t}+c_{2}e^{-t}-2t^2+5t-9/2