What is the solution for x^2y^'+x(x+2)y=ex ?

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

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x^2y^'+x(x+2)y=ex

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

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

Solution steps

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

Solve linear ODE:

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

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

x \to 0 lim (3^{s i n (\frac{1}{x})})

\frac{d y}{d x} + \frac{1}{x} y = 2

\frac{d}{d x} (3^{l n (x)})

\int \frac{2 - x}{2} d x

\frac{d}{d x} (\frac{x - 9}{4 x ^{2} e ^{x}})

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