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

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

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

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

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

Solution steps

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

Solve linear ODE:

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

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

\frac{6}{( w ^{2} - 8 ) ^{4}}

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x \to π lim (π - x (csc (x)))

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