What is the solution for 5y^{''}+y^'=-10x ?

The solution for 5y^{''}+y^'=-10x is y=c_{1}+c_{2}e^{-x/5}-5x^2+50x

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5y^{''}+y^'=-10x

5 y^{^{''}} + y^{^{'}} = - 10 x

y = c_{1} + c_{2} e^{- \frac{x}{5}} - 5 x^{2} + 50 x

Solution steps

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

Solve linear ODE:

y = c_{1} + c_{2} e^{- \frac{x}{5}} - 5 x^{2} + 50 x

y = c_{1} + c_{2} e^{- \frac{x}{5}} - 5 x^{2} + 50 x

\frac{4 x}{x + 2}

\int x e^{x - 2} d x

\int \frac{1}{( 4 + x ^{2} )} d x

x \to 0 lim (\frac{3 x}{2 x ^{2} - x})

\frac{( x + 4 ) ( x ^{2} - 4 x + 16 )}{x ^{3}}

What is the solution for 5y^{''}+y^'=-10x ?
The solution for 5y^{''}+y^'=-10x is y=c_{1}+c_{2}e^{-x/5}-5x^2+50x