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

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

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xy-(dx)/(dy)=-x^2(dx)/(dy)

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

y = - x^{2} + 2 ln (x) + c_{1}, y = - - x^{2} + 2 ln (x) + c_{1}

Solution steps

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

Solve separable ODE:

y = - x^{2} + 2 ln (x) + c_{1}, y = - - x^{2} + 2 ln (x) + c_{1}

y = - x^{2} + 2 ln (x) + c_{1}, y = - - x^{2} + 2 ln (x) + c_{1}

\frac{d y}{d x} = 2 x y^{2} + 5 \frac{y ^{2}}{x}

\frac{d p}{d t} = p (2 p - 1)

sin (x) y^{^{'}} + y = 0

2 y + 3 + (2 x - 3) \frac{d y}{d x} = 0

(4 + x^{2}) \frac{d y}{d x} + 2 x y = 4 x

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