What is the solution for (d^2y)/(dx^2)-2(dy)/(dx)+y=(e^x)/(x^5) ?

The solution for (d^2y)/(dx^2)-2(dy)/(dx)+y=(e^x)/(x^5) is y=c_{1}e^x+c_{2}xe^x+(e^x)/(12x^3)

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(d^2y)/(dx^2)-2(dy)/(dx)+y=(e^x)/(x^5)

\frac{d ^{2} y}{d x ^{2}} - 2 \frac{d y}{d x} + y = \frac{e ^{x}}{x ^{5}}

y = c_{1} e^{x} + c_{2} x e^{x} + \frac{e ^{x}}{12 x ^{3}}

Solution steps

\frac{d ^{2} y}{d x ^{2}} - 2 \frac{d y}{d x} + y = \frac{e ^{x}}{x ^{5}}

Solve linear ODE:

y = c_{1} e^{x} + c_{2} x e^{x} + \frac{e ^{x}}{12 x ^{3}}

y = c_{1} e^{x} + c_{2} x e^{x} + \frac{e ^{x}}{12 x ^{3}}

What is the solution for (d^2y)/(dx^2)-2(dy)/(dx)+y=(e^x)/(x^5) ?
The solution for (d^2y)/(dx^2)-2(dy)/(dx)+y=(e^x)/(x^5) is y=c_{1}e^x+c_{2}xe^x+(e^x)/(12x^3)