What is the solution for 5y^{''}+y^'=-2x,y(0)=0,y^'(0)=-20 ?

The solution for 5y^{''}+y^'=-2x,y(0)=0,y^'(0)=-20 is y=-150+150e^{-x/5}-x^2+10x

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5y^{''}+y^'=-2x,y(0)=0,y^'(0)=-20

5 y^{^{''}} + y^{^{'}} = - 2 x, y (0) = 0, y^{^{'}} (0) = - 20

y = - 150 + 150 e^{- \frac{x}{5}} - x^{2} + 10 x

Solution steps

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

Solve linear ODE:

y = - 150 + 150 e^{- \frac{x}{5}} - x^{2} + 10 x

y = - 150 + 150 e^{- \frac{x}{5}} - x^{2} + 10 x

4 y^{^{''}} - 4 y^{^{'}} + y = e^{\frac{x}{2}}

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

y^{^{''}} - 4 y^{^{'}} + 13 (t) = 0

y^{^{''}} - y^{^{'}} = 2 e^{- t}, y (0) = 0, y^{^{'}} (0) = 0

y^{^{''}} + 9 y = 12 cos (3 t)

What is the solution for 5y^{''}+y^'=-2x,y(0)=0,y^'(0)=-20 ?
The solution for 5y^{''}+y^'=-2x,y(0)=0,y^'(0)=-20 is y=-150+150e^{-x/5}-x^2+10x