What is the solution for y^{''}-2y^'+y=(e^x)/(x^3) ?

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

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y^{''}-2y^'+y=(e^x)/(x^3)

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

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

Solution steps

y^{''} (x) - 2 y^{'} (x) + y = \frac{e ^{x}}{x ^{3}}

Solve linear ODE:

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

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

y^{^{''}} + 4 y = 4 csc^{2} (2 t)

\frac{d ^{2} y}{d x ^{2}} - 5 \frac{d y}{d x} + 4 y = e^{x}

y^{^{'''}} - y^{^{''}} - 25 y^{^{'}} + 25 y = 7 - e^{x} + e^{5 x}

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

y^{^{''}} - 8 y^{^{'}} + 15 y = e^{3 x} sin (3 x)

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