What is the solution for 5y^{''}+y^'=-6x,y(0)=0,y^'(0)=-10 ?

The solution for 5y^{''}+y^'=-6x,y(0)=0,y^'(0)=-10 is y=-200+200e^{-x/5}-3x^2+30x

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5y^{''}+y^'=-6x,y(0)=0,y^'(0)=-10

5 y^{^{''}} + y^{^{'}} = - 6 x, y (0) = 0, y^{^{'}} (0) = - 10

y = - 200 + 200 e^{- \frac{x}{5}} - 3 x^{2} + 30 x

Solution steps

5 y^{''} (x) + y^{'} (x) = - 6 x

Solve linear ODE:

y = - 200 + 200 e^{- \frac{x}{5}} - 3 x^{2} + 30 x

y = - 200 + 200 e^{- \frac{x}{5}} - 3 x^{2} + 30 x

y^{^{'''}} + y^{^{'}} = sin (x)

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

y^{^{''}} + 2 y^{^{'}} + y = \frac{ln ( x )}{e ^{x}}

y^{^{''}} - y^{^{'}} - 2 y = \frac{( e ^{2 t} + e ^{- 2 t} )}{2}

\frac{d ^{2} y}{d x ^{2}} - 3 y = e^{2 x} sin (x)

What is the solution for 5y^{''}+y^'=-6x,y(0)=0,y^'(0)=-10 ?
The solution for 5y^{''}+y^'=-6x,y(0)=0,y^'(0)=-10 is y=-200+200e^{-x/5}-3x^2+30x