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

The solution for x^2((dy)/(dx))+x(x+2)y=e^x is y=(e^x)/(2x^2)+(c_{1})/(e^xx^2)

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

x^{2} (\frac{d y}{d x}) + x (x + 2) y = e^{x}

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

Solution steps

x^{2} (\frac{d y}{d x}) + x (x + 2) y = e^{x}

Solve linear ODE:

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

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

f (x) = sec (4 x)

\int x \cdot ln (x^{6}) d x

x \to \infty lim (9 + \frac{8}{x})

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