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

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

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

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

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

Solution steps

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

Solve separable ODE:

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

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

\frac{y d y}{d x} + 4 x^{2} + 6 x + 1 = 0

y^{^{'}} = e^{3 x - 4 y}, y (0) = 0

\frac{d y}{d x} + 9 x^{8} y = 0, y = 6 e^{- x^{9}}

e^{y} y^{^{'}} = 1, y (0) = ln (x + c)

y^{^{'}} = x y^{2} sin (x), y (0) = 2

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