What is the solution for (d^3y)/(dx^3)-(d^2y)/(dx^2)=e^x ?

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

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(d^3y)/(dx^3)-(d^2y)/(dx^2)=e^x

\frac{d ^{3} y}{d x ^{3}} - \frac{d ^{2} y}{d x ^{2}} = e^{x}

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

Solution steps

\frac{d ^{3} y}{d x ^{3}} - \frac{d ^{2} y}{d x ^{2}} = e^{x}

Solve linear ODE:

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

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

x^{^{''}} - 18 x^{^{'}} + 81 x = t e^{9 t}

x^{^{''}} - 4 x^{^{'}} - 5 x = 2 + e^{- t}

\frac{d ^{2} y}{d x ^{2}} - 6 \frac{d y}{d x} + 9 y = 9 x

y^{^{''}} + 9 y^{^{'}} + 22 y = e^{- 3 x}

(D^{2} - 4 D + 5) y = (x + 1)^{3}

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