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

The solution for 5y^{''}+y^'=-6x,y(0)=0,y^'(0)=-5 is y=-175+175e^{-x/5}-3x^2+30x

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

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

y = - 175 + 175 e^{- \frac{x}{5}} - 3 x^{2} + 30 x

Solution steps

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

Solve linear ODE:

y = - 175 + 175 e^{- \frac{x}{5}} - 3 x^{2} + 30 x

y = - 175 + 175 e^{- \frac{x}{5}} - 3 x^{2} + 30 x

What is the solution for 5y^{''}+y^'=-6x,y(0)=0,y^'(0)=-5 ?
The solution for 5y^{''}+y^'=-6x,y(0)=0,y^'(0)=-5 is y=-175+175e^{-x/5}-3x^2+30x