What is the solution for x^2y^'+3xy=e^x ?

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

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x^2y^'+3xy=e^x

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

y = \frac{e ^{x}}{x ^{2}} - \frac{e ^{x}}{x ^{3}} + \frac{c _{1}}{x ^{3}}

Solution steps

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

Solve linear ODE:

y = \frac{e ^{x}}{x ^{2}} - \frac{e ^{x}}{x ^{3}} + \frac{c _{1}}{x ^{3}}

y = \frac{e ^{x}}{x ^{2}} - \frac{e ^{x}}{x ^{3}} + \frac{c _{1}}{x ^{3}}

2 y^{^{''}} - 2 y^{^{'}} + 13 y = 0

\frac{d}{d x} (- 4 sin^{3} (3 x))

\int \frac{1}{5000 x - x ^{2}} d x

\int_{0}^{9} 2 x + 8 - x d x

\int_{0}^{\frac{π}{4}} 1 - 4 sin^{2} (x) d x

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