What is the solution for y^{''}-y^'-2y=-6t+10t^2 ?

The solution for y^{''}-y^'-2y=-6t+10t^2 is y=c_{1}e^{2t}+c_{2}e^{-t}-5t^2+8t-9

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y^{''}-y^'-2y=-6t+10t^2

y^{^{''}} - y^{^{'}} - 2 y = - 6 t + 10 t^{2}

y = c_{1} e^{2 t} + c_{2} e^{- t} - 5 t^{2} + 8 t - 9

Solution steps

y^{''} (t) - y^{'} (t) - 2 y = - 6 t + 10 t^{2}

Solve linear ODE:

y = c_{1} e^{2 t} + c_{2} e^{- t} - 5 t^{2} + 8 t - 9

y = c_{1} e^{2 t} + c_{2} e^{- t} - 5 t^{2} + 8 t - 9

\frac{1 + e ^{- s π}}{s ^{2} + 1}

y = 3 e^{3 e^{x} + x}

tan (x), 2 sin (x), [- \frac{π}{3}, \frac{π}{3}]

\frac{\partial}{\partial x} (e^{- 2 x})

\frac{d}{d x} ((4 x)^{3 x})

What is the solution for y^{''}-y^'-2y=-6t+10t^2 ?
The solution for y^{''}-y^'-2y=-6t+10t^2 is y=c_{1}e^{2t}+c_{2}e^{-t}-5t^2+8t-9