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

The solution for y^{''}-6y^'+5y=x is y=c_{1}e^{5x}+c_{2}e^x+x/5+6/25

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

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

y = c_{1} e^{5 x} + c_{2} e^{x} + \frac{x}{5} + \frac{6}{25}

Solution steps

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

Solve linear ODE:

y = c_{1} e^{5 x} + c_{2} e^{x} + \frac{x}{5} + \frac{6}{25}

y = c_{1} e^{5 x} + c_{2} e^{x} + \frac{x}{5} + \frac{6}{25}

y^{^{''}} + 3 y^{^{'}} + 5 y = 4 t + 2 + e^{7 t}

y^{^{'''}} - y^{^{''}} - 16 y^{^{'}} + 16 y = 3 - e^{x} + e^{4 x}

y^{^{''}} - 6 y^{^{'}} + 9 y = 3 x^{2} + 4 e^{4 x}

y^{^{''}} + 4 y^{^{'}} + 3 y = 8 x e^{x} - 6

y^{^{''}} + 3 y^{^{'}} - 10 y = e^{- 5 x}

What is the solution for y^{''}-6y^'+5y=x ?
The solution for y^{''}-6y^'+5y=x is y=c_{1}e^{5x}+c_{2}e^x+x/5+6/25