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

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

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

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

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

Solution steps

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

Solve linear ODE:

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

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

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

y^{^{'''}} - 21 y^{^{''}} + 1372 y = e^{14 x}

y^{^{''}} + 2 y^{^{'}} - 3 y = 4 e^{- 3 x}

(D^{2} - 1) y = e^{x} + 1

y^{^{''}} + 3 y^{^{'}} - 4 y = 2, y (0) = 0

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