What is the solution for 5y^{''}+y^'=-2x,y(0)=0,y^'(0)=-15 ?

The solution for 5y^{''}+y^'=-2x,y(0)=0,y^'(0)=-15 is y=-125+125e^{-x/5}-x^2+10x

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5y^{''}+y^'=-2x,y(0)=0,y^'(0)=-15

5 y^{^{''}} + y^{^{'}} = - 2 x, y (0) = 0, y^{^{'}} (0) = - 15

y = - 125 + 125 e^{- \frac{x}{5}} - x^{2} + 10 x

Solution steps

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

Solve linear ODE:

y = - 125 + 125 e^{- \frac{x}{5}} - x^{2} + 10 x

y = - 125 + 125 e^{- \frac{x}{5}} - x^{2} + 10 x

\frac{d}{d x} (\frac{1}{e ^{2 x}})

(x + \frac{1}{3 x})^{2}

y = 6 x + x^{2}

\int \frac{1}{t ^{2} 6 - t ^{2}} d t

f (x) = cos (a^{5} + x^{5})

What is the solution for 5y^{''}+y^'=-2x,y(0)=0,y^'(0)=-15 ?
The solution for 5y^{''}+y^'=-2x,y(0)=0,y^'(0)=-15 is y=-125+125e^{-x/5}-x^2+10x