Equation of a curve with given equation of slope and passing through a point

Problem
What is the equation of the curve passing through the point (3, -2) and having a slope at any point (x, y) equal to (x2 + y2) / (y3 - 2xy)?
 

Solution

 

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Comments

Excuse me sir isnt it

Excuse me sir isnt it supposed to be 2(y^2)(x) when integrating from the right side

Please indicate which line of

Please indicate which line of the solution you are referring to for us to locate your concern.
 

$\dfrac{dy}{dx} = \dfrac{x^2 + y^2}{y^3 - 2xy}$   ←   Line (1)

$(y^3 - 2xy) \, dy = (x^2 + y^2) \, dx$   ←   Line (2)

$y^3 \, dy - 2xy \, dy = x^2 \, dx + y^2 \, dx$   ←   Line (3)

$y^3 \, dy - x^2 \, dx = x(2y \, dy) + y^2 \, dx$   ←   Line (4)

$y^3 \, dy - x^2 \, dx = x(2y \, dy) + y^2 \, dx$   ←   Line (5)

$y^3 \, dy - x^2 \, dx = d(xy^2)$   ←   Line (6)

$\displaystyle \int y^3 \, dy - \int x^2 \, dx = \int d(xy^2)$   ←   Line (7)

Integrating from the right

Integrating from the right side at line 6 sir isnt it suppose to be (x)(y^2)+(x)(y)

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