What is the solution for 5y^{''}+y^'=-4x,y(0)=0 ?

The solution for 5y^{''}+y^'=-4x,y(0)=0 is y=-c_{2}+c_{2}e^{-x/5}-2x^2+20x

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5y^{''}+y^'=-4x,y(0)=0

5 y^{^{''}} + y^{^{'}} = - 4 x, y (0) = 0

y = - c_{2} + c_{2} e^{- \frac{x}{5}} - 2 x^{2} + 20 x

Solution steps

5 y^{''} (x) + y^{'} (x) = - 4 x

Solve linear ODE:

y = - c_{2} + c_{2} e^{- \frac{x}{5}} - 2 x^{2} + 20 x

y = - c_{2} + c_{2} e^{- \frac{x}{5}} - 2 x^{2} + 20 x

What is the solution for 5y^{''}+y^'=-4x,y(0)=0 ?
The solution for 5y^{''}+y^'=-4x,y(0)=0 is y=-c_{2}+c_{2}e^{-x/5}-2x^2+20x