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

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

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

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

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

Solution steps

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

Solve linear ODE:

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

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

y^{^{'}} + 2 y = x

\int - 5 x^{2} d x

\frac{d}{d x} (\frac{( x ^{2} + 1 )}{x + 4})

\frac{d}{d x} ((x - 1)^{2} - (x^{2} + 1)^{4})

\int t e^{t + 2} d t

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