What is the solution for y^{''}=-0.1y^'-x ?

The solution for y^{''}=-0.1y^'-x is y=c_{1}+c_{2}e^{-x/(10)}-5x^2+100x

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y^{''}=-0.1y^'-x

y^{^{''}} = - 0.1 y^{^{'}} - x

y = c_{1} + c_{2} e^{- \frac{x}{10}} - 5 x^{2} + 100 x

Solution steps

y^{''} (x) = - 0.1 y^{'} (x) - x

Solve linear ODE:

y = c_{1} + c_{2} e^{- \frac{x}{10}} - 5 x^{2} + 100 x

y = c_{1} + c_{2} e^{- \frac{x}{10}} - 5 x^{2} + 100 x

y^{^{''}} + 4 y = g (t)

y^{^{''}} - 3 y^{^{'}} = 2 x - 3

y^{^{'''}} - 6 y^{^{''}} + 8 y^{^{'}} = sin (2 t) + t^{2} e^{t}

y^{^{''}} - 6 y^{^{'}} + 9 y = 15 x + 4

y^{^{''}} + y = 2 x \cdot e^{x} - 2 sin (x)

What is the solution for y^{''}=-0.1y^'-x ?
The solution for y^{''}=-0.1y^'-x is y=c_{1}+c_{2}e^{-x/(10)}-5x^2+100x