What is the solution for y^{'''}-3y^{''}+3y^'-y=x-7e^x ?

The solution for y^{'''}-3y^{''}+3y^'-y=x-7e^x is y=c_{1}e^x+c_{2}xe^x+c_{3}x^2e^x-x-3-(7e^xx^3)/6

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y^{'''}-3y^{''}+3y^'-y=x-7e^x

y^{^{'''}} - 3 y^{^{''}} + 3 y^{^{'}} - y = x - 7 e^{x}

y = c_{1} e^{x} + c_{2} x e^{x} + c_{3} x^{2} e^{x} - x - 3 - \frac{7 e ^{x} x ^{3}}{6}

Solution steps

y^{'''} (x) - 3 y^{''} (x) + 3 y^{'} (x) - y = x - 7 e^{x}

Solve linear ODE:

y = c_{1} e^{x} + c_{2} x e^{x} + c_{3} x^{2} e^{x} - x - 3 - \frac{7 e ^{x} x ^{3}}{6}

y = c_{1} e^{x} + c_{2} x e^{x} + c_{3} x^{2} e^{x} - x - 3 - \frac{7 e ^{x} x ^{3}}{6}

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\frac{d}{d x} (6 x^{2} cos (x) cot (x))

n = 1 \sum \infty \frac{1}{n ^{3} + 1}

\int \frac{( 3 x ^{4} )}{( x ^{2} - 2 x )} d x

What is the solution for y^{'''}-3y^{''}+3y^'-y=x-7e^x ?
The solution for y^{'''}-3y^{''}+3y^'-y=x-7e^x is y=c_{1}e^x+c_{2}xe^x+c_{3}x^2e^x-x-3-(7e^xx^3)/6