What is the solution for y^{''}+y^'-30y=2x ?

The solution for y^{''}+y^'-30y=2x is y=c_{1}e^{5x}+c_{2}e^{-6x}-x/(15)-1/450

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y^{''}+y^'-30y=2x

y^{^{''}} + y^{^{'}} - 30 y = 2 x

y = c_{1} e^{5 x} + c_{2} e^{- 6 x} - \frac{x}{15} - \frac{1}{450}

Solution steps

y^{''} (x) + y^{'} (x) - 30 y = 2 x

Solve linear ODE:

y = c_{1} e^{5 x} + c_{2} e^{- 6 x} - \frac{x}{15} - \frac{1}{450}

y = c_{1} e^{5 x} + c_{2} e^{- 6 x} - \frac{x}{15} - \frac{1}{450}

y^{^{'''}} - y^{^{''}} - 4 y^{^{'}} + 4 y = 5 - e^{x} + e^{2 x}

y^{^{''}} + 16 y = t^{2} + 1

y^{^{''}} - 2 y^{^{'}} + y = 3 x^{2} - 5

y^{^{''}} - 7 y^{^{'}} = t^{2}

y^{^{''}} - y^{^{'}} + 2 = 0

What is the solution for y^{''}+y^'-30y=2x ?
The solution for y^{''}+y^'-30y=2x is y=c_{1}e^{5x}+c_{2}e^{-6x}-x/(15)-1/450