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}

(D^{2} + 2 D - 3) y = cos (2 x)

y^{^{''}} - 8 y^{^{'}} = 6 e^{2 x} - 6 x^{2} - 9 x - 14

y^{^{''}} + 10 y^{^{'}} + 41 = 0

y^{^{''}} - 3 y^{^{'}} + 4 y = 16 x - 50 cos (2 x)

y^{^{''}} - y^{^{'}} - 3 y - 4 = 0

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)