What is the solution for y^{'''}-3y^{''}=9e^x ?

The solution for y^{'''}-3y^{''}=9e^x is y=c_{1}e^{3x}+c_{2}+c_{3}x-9/2 e^x

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y^{'''}-3y^{''}=9e^x

y^{^{'''}} - 3 y^{^{''}} = 9 e^{x}

y = c_{1} e^{3 x} + c_{2} + c_{3} x - \frac{9}{2} e^{x}

Solution steps

y^{'''} (x) - 3 y^{''} (x) = 9 e^{x}

Solve linear ODE:

y = c_{1} e^{3 x} + c_{2} + c_{3} x - \frac{9}{2} e^{x}

y = c_{1} e^{3 x} + c_{2} + c_{3} x - \frac{9}{2} e^{x}

y^{^{''}} + 2 y^{^{'}} + 2 y = e^{- t} sin (3 t)

y^{^{''}} - 4 y^{^{'}} + 5 y = e^{2 x} csc (x)

y^{^{''}} + 4 y = u_{π} (t) - u_{3 π} (t)

y^{^{''}} - 2 y^{^{'}} + y = cos (3 x)

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

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