What is the solution for y^{''}-4y^'-5y=5x ?

The solution for y^{''}-4y^'-5y=5x is y=c_{1}e^{5x}+c_{2}e^{-x}-x+4/5

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y^{''}-4y^'-5y=5x

y^{^{''}} - 4 y^{^{'}} - 5 y = 5 x

y = c_{1} e^{5 x} + c_{2} e^{- x} - x + \frac{4}{5}

Solution steps

y^{''} (x) - 4 y^{'} (x) - 5 y = 5 x

Solve linear ODE:

y = c_{1} e^{5 x} + c_{2} e^{- x} - x + \frac{4}{5}

y = c_{1} e^{5 x} + c_{2} e^{- x} - x + \frac{4}{5}

\int \frac{1}{s ^{2} ( s - 1 ) ^{2}} d s

\int 6 x^{2} + 1 d x

x \to 0 + lim (- \frac{1}{x ^{2}})

y^{^{''}} - 5 y^{^{'}} + 9 y = x e^{x}

\frac{d}{d x} ((x^{2} - 2 x - 1)^{\frac{2}{3}})

What is the solution for y^{''}-4y^'-5y=5x ?
The solution for y^{''}-4y^'-5y=5x is y=c_{1}e^{5x}+c_{2}e^{-x}-x+4/5