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

The solution for 5y^{''}+y^'=-6x is y=c_{1}+c_{2}e^{-x/5}-3x^2+30x

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

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

y = c_{1} + c_{2} e^{- \frac{x}{5}} - 3 x^{2} + 30 x

Solution steps

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

Solve linear ODE:

y = c_{1} + c_{2} e^{- \frac{x}{5}} - 3 x^{2} + 30 x

y = c_{1} + c_{2} e^{- \frac{x}{5}} - 3 x^{2} + 30 x

\frac{\partial}{\partial x} (y - 3 x)

x \to 0 lim (\frac{x}{sin ( π x )})

x \to - \infty lim (x^{5})

x \to 1 lim (3 x^{2} + 2 x + 1)

\frac{d}{d x} (x cos (\frac{1}{x}))

What is the solution for 5y^{''}+y^'=-6x ?
The solution for 5y^{''}+y^'=-6x is y=c_{1}+c_{2}e^{-x/5}-3x^2+30x