What is the solution for y^{'''}-11y^{''}+28y^'=90e^x ?

The solution for y^{'''}-11y^{''}+28y^'=90e^x is y=c_{1}+c_{2}e^{4x}+c_{3}e^{7x}+5e^x

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y^{'''}-11y^{''}+28y^'=90e^x

y^{^{'''}} - 11 y^{^{''}} + 28 y^{^{'}} = 90 e^{x}

y = c_{1} + c_{2} e^{4 x} + c_{3} e^{7 x} + 5 e^{x}

Solution steps

y^{'''} (x) - 11 y^{''} (x) + 28 y^{'} (x) = 90 e^{x}

Solve linear ODE:

y = c_{1} + c_{2} e^{4 x} + c_{3} e^{7 x} + 5 e^{x}

y = c_{1} + c_{2} e^{4 x} + c_{3} e^{7 x} + 5 e^{x}

What is the solution for y^{'''}-11y^{''}+28y^'=90e^x ?
The solution for y^{'''}-11y^{''}+28y^'=90e^x is y=c_{1}+c_{2}e^{4x}+c_{3}e^{7x}+5e^x