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

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

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(d^2y}{dx^2}-2(dy)/(dx)+y=\frac{e^x)/x

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

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

Solution steps

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

Solve linear ODE:

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

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

\frac{d ^{2} y}{d x ^{2}} + 2 \frac{d y}{d x} + 4 y = cos (4 x)

5 y^{^{''}} - 40 y^{^{'}} + 35 y = 26 x

y^{^{''}} + 20 y^{^{'}} + 2600 y = 1000 sin (60 t)

y^{^{''}} + 13 y = 4 e^{9 x}

(D^{2} + 4 D - 12) y = sin^{2} (x)

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