What is the solution for y^{'''}-13y^{''}+36y^'=72e^x ?

The solution for y^{'''}-13y^{''}+36y^'=72e^x is y=c_{1}+c_{2}e^{4x}+c_{3}e^{9x}+3e^x

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y^{'''}-13y^{''}+36y^'=72e^x

y^{^{'''}} - 13 y^{^{''}} + 36 y^{^{'}} = 72 e^{x}

y = c_{1} + c_{2} e^{4 x} + c_{3} e^{9 x} + 3 e^{x}

Solution steps

y^{'''} (x) - 13 y^{''} (x) + 36 y^{'} (x) = 72 e^{x}

Solve linear ODE:

y = c_{1} + c_{2} e^{4 x} + c_{3} e^{9 x} + 3 e^{x}

y = c_{1} + c_{2} e^{4 x} + c_{3} e^{9 x} + 3 e^{x}

What is the solution for y^{'''}-13y^{''}+36y^'=72e^x ?
The solution for y^{'''}-13y^{''}+36y^'=72e^x is y=c_{1}+c_{2}e^{4x}+c_{3}e^{9x}+3e^x