What is the solution for (dy)/(dx)+xy= x/(y^2),y(1)=0.5 ?

The solution for (dy)/(dx)+xy= x/(y^2),y(1)=0.5 is y=(\sqrt[3]{-7e^{(-3x^2+3)/2}+8})/(2)

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(dy)/(dx)+xy= x/(y^2),y(1)=0.5

\frac{d y}{d x} + x y = \frac{x}{y ^{2}}, y (1) = 0.5

y = \frac{3 - 7 e ^{\frac{- 3 x ^{2} + 3}{2}} + 8}{2}

Solution steps

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

Solve separable ODE:

y = \frac{3 - 7 e ^{\frac{- 3 x ^{2} + 3}{2}} + 8}{2}

y = \frac{3 - 7 e ^{\frac{- 3 x ^{2} + 3}{2}} + 8}{2}

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

(3 x + 8) (y^{2} + 4) d x - 4 y (x^{2} + 5 x + 6) d y = 0

\frac{d y}{d x} = \frac{y ln ( x )}{x}

y^{^{'}} = x y^{3} (1 + x^{2})^{- \frac{1}{2}}, y (0) = 1

y^{^{'}} + ln (x) y = 3 ln (x)

What is the solution for (dy)/(dx)+xy= x/(y^2),y(1)=0.5 ?
The solution for (dy)/(dx)+xy= x/(y^2),y(1)=0.5 is y=(\sqrt[3]{-7e^{(-3x^2+3)/2}+8})/(2)