What is the solution for x^2(dy)/(dx)+4xy-e^x=0 ?

The solution for x^2(dy)/(dx)+4xy-e^x=0 is y=(e^x)/(x^2)-(2(e^xx-e^x))/(x^4)+(c_{1})/(x^4)

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x^2(dy)/(dx)+4xy-e^x=0

x^{2} \frac{d y}{d x} + 4 x y - e^{x} = 0

y = \frac{e ^{x}}{x ^{2}} - \frac{2 ( e ^{x} x - e ^{x} )}{x ^{4}} + \frac{c _{1}}{x ^{4}}

Solution steps

x^{2} \frac{d y}{d x} + 4 x y - e^{x} = 0

Solve linear ODE:

y = \frac{e ^{x}}{x ^{2}} - \frac{2 ( e ^{x} x - e ^{x} )}{x ^{4}} + \frac{c _{1}}{x ^{4}}

y = \frac{e ^{x}}{x ^{2}} - \frac{2 ( e ^{x} x - e ^{x} )}{x ^{4}} + \frac{c _{1}}{x ^{4}}

(2 y - 8 x^{2}) d x + x d y = 0

\frac{d}{d x} (e^{x \cdot s i n (x)})

x \to 2 + lim (\frac{1}{x - 2})

f (x) = (arcsin (5 x + 3))^{3}

y^{^{''}} - y^{^{'}} - 2 y = x^{2}

What is the solution for x^2(dy)/(dx)+4xy-e^x=0 ?
The solution for x^2(dy)/(dx)+4xy-e^x=0 is y=(e^x)/(x^2)-(2(e^xx-e^x))/(x^4)+(c_{1})/(x^4)