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

y^{^{''}} - 8 y^{^{'}} + 17 y = e^{4 x} - x^{2}

y^{^{''}} - 81 y = e^{10} t

y^{^{''}} - 7 y^{^{'}} + 6 y = sin (x)

3 \frac{d ^{2} y}{d x ^{2}} + \frac{d y}{d x} - 4 y = 10 e^{- 3 x}

y^{^{''}} + 7 y^{^{'}} + 6 y = 8

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