What is the solution for y^{''}+2y^'-15y=-53t+30t^2 ?

The solution for y^{''}+2y^'-15y=-53t+30t^2 is y=c_{1}e^{3t}+c_{2}e^{-5t}-2t^2+3t+2/15

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y^{''}+2y^'-15y=-53t+30t^2

y^{^{''}} + 2 y^{^{'}} - 15 y = - 53 t + 30 t^{2}

y = c_{1} e^{3 t} + c_{2} e^{- 5 t} - 2 t^{2} + 3 t + \frac{2}{15}

Solution steps

y^{''} (t) + 2 y^{'} (t) - 15 y = - 53 t + 30 t^{2}

Solve linear ODE:

y = c_{1} e^{3 t} + c_{2} e^{- 5 t} - 2 t^{2} + 3 t + \frac{2}{15}

y = c_{1} e^{3 t} + c_{2} e^{- 5 t} - 2 t^{2} + 3 t + \frac{2}{15}

y^{^{''}} - 2 y^{^{'}} + 5 y = e^{x}, y (0) = 0, y^{^{'}} (0) = 0

y^{^{''}} - 6 y^{^{'}} + 9 y = x^{(- 3)} e^{3} x

x^{^{''}} + 2 x + 3 x^{^{'}} = 5 cos (t) + sin (2 t)

(D^{2} + 2 D + 1) y = e^{- x}

y^{^{''}} - y^{^{'}} = 4 x e^{x}, y (0) = 0, y^{^{'}} (0) = 1

What is the solution for y^{''}+2y^'-15y=-53t+30t^2 ?
The solution for y^{''}+2y^'-15y=-53t+30t^2 is y=c_{1}e^{3t}+c_{2}e^{-5t}-2t^2+3t+2/15