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}}

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)