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

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

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

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

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

Solution steps

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

Solve linear ODE:

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

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

x \to \infty lim (x sin (\frac{3 π}{x}))

\int_{1}^{4} y ln (y) d y

\frac{d x}{d t} = k x (1000 - x)

y^{^{''}} + 400 y = sec (20 x), y (0) = 5, y^{^{'}} (0) = - 5

\int (x - 1) sec^{2} (x) d x

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