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

The solution for y^{''}+6y^'=5x is y=c_{1}+c_{2}e^{-6x}+(5x^2)/(12)-(5x)/(36)

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

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

y = c_{1} + c_{2} e^{- 6 x} + \frac{5 x ^{2}}{12} - \frac{5 x}{36}

Solution steps

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

Solve linear ODE:

y = c_{1} + c_{2} e^{- 6 x} + \frac{5 x ^{2}}{12} - \frac{5 x}{36}

y = c_{1} + c_{2} e^{- 6 x} + \frac{5 x ^{2}}{12} - \frac{5 x}{36}

What is the solution for y^{''}+6y^'=5x ?
The solution for y^{''}+6y^'=5x is y=c_{1}+c_{2}e^{-6x}+(5x^2)/(12)-(5x)/(36)