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

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

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

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

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

Solution steps

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

Solve linear ODE:

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

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

y^{^{''}} - 5 y^{^{'}} + 4 y = e^{4 t}

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

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

y^{^{'''}} + 25 y^{^{'}} = tan (5 x)

y^{^{''}} - 5 y^{^{'}} + 6 y = (x + 1)^{2} e^{2 x}

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