What is the solution for y^{''}+10y^'+25y=-8-5x+25x^2 ?

The solution for y^{''}+10y^'+25y=-8-5x+25x^2 is y=c_{1}e^{-5x}+c_{2}xe^{-5x}+x^2-x

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y^{''}+10y^'+25y=-8-5x+25x^2

y^{^{''}} + 10 y^{^{'}} + 25 y = - 8 - 5 x + 25 x^{2}

y = c_{1} e^{- 5 x} + c_{2} x e^{- 5 x} + x^{2} - x

Solution steps

y^{''} (x) + 10 y^{'} (x) + 25 y = - 8 - 5 x + 25 x^{2}

Solve linear ODE:

y = c_{1} e^{- 5 x} + c_{2} x e^{- 5 x} + x^{2} - x

y = c_{1} e^{- 5 x} + c_{2} x e^{- 5 x} + x^{2} - x

10 x^{^{''}} + 200 x = 600 sin (125 t)

5 y^{^{''}} + 6 y^{^{'}} + y = x^{3} + 18 x^{2} + 32 x + 13

y^{^{''}} - 6 y^{^{'}} + 8 y = 3 + e^{- 2 t}

\frac{d ^{2} y}{d x ^{2}} - y = cosh (x) + x

y^{^{''}} - y^{^{'}} = e^{2 x}

What is the solution for y^{''}+10y^'+25y=-8-5x+25x^2 ?
The solution for y^{''}+10y^'+25y=-8-5x+25x^2 is y=c_{1}e^{-5x}+c_{2}xe^{-5x}+x^2-x