What is the solution for y^{''}-2y^'-35y=-97t+70t^2 ?

The solution for y^{''}-2y^'-35y=-97t+70t^2 is y=c_{1}e^{7t}+c_{2}e^{-5t}-2t^2+3t-2/7

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y^{''}-2y^'-35y=-97t+70t^2

y^{^{''}} - 2 y^{^{'}} - 35 y = - 97 t + 70 t^{2}

y = c_{1} e^{7 t} + c_{2} e^{- 5 t} - 2 t^{2} + 3 t - \frac{2}{7}

Solution steps

y^{''} (t) - 2 y^{'} (t) - 35 y = - 97 t + 70 t^{2}

Solve linear ODE:

y = c_{1} e^{7 t} + c_{2} e^{- 5 t} - 2 t^{2} + 3 t - \frac{2}{7}

y = c_{1} e^{7 t} + c_{2} e^{- 5 t} - 2 t^{2} + 3 t - \frac{2}{7}

y^{^{'''}} + y^{^{''}} = 7 x^{2}

(D^{2} - 2 D + 2) y = 3 e^{x} sin (x)

y^{^{''}} + 9 y = sin (x) - 2

y^{^{'''}} - y^{^{'}} = tan (x)

y^{^{''}} + 4 y^{^{'}} + 8 y = 12 e^{- 2 x} sec (2 x)

What is the solution for y^{''}-2y^'-35y=-97t+70t^2 ?
The solution for y^{''}-2y^'-35y=-97t+70t^2 is y=c_{1}e^{7t}+c_{2}e^{-5t}-2t^2+3t-2/7