What is the solution for (xy-y^2)dx+x^3dy=0 ?

The solution for (xy-y^2)dx+x^3dy=0 is y=(xe^{1/x})/(e^{1/x)-e^{1/x}x+c_{1}x}

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(xy-y^2)dx+x^3dy=0

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

y = \frac{x e ^{\frac{1}{x}}}{e ^{\frac{1}{x}} - e ^{\frac{1}{x}} x + c _{1} x}

Solution steps

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

Solve Bernoulli ODE:

y = \frac{x e ^{\frac{1}{x}}}{e ^{\frac{1}{x}} - e ^{\frac{1}{x}} x + c _{1} x}

y = \frac{x e ^{\frac{1}{x}}}{e ^{\frac{1}{x}} - e ^{\frac{1}{x}} x + c _{1} x}

t an g e n t f (x) = 3 x^{2} - 3 x

d er i v a t i v e y = \frac{x}{1 + x}

s l o p e (0, - 3), (- 3, 0)

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

\frac{\partial}{\partial x} (\frac{( 2 x )}{y})

What is the solution for (xy-y^2)dx+x^3dy=0 ?
The solution for (xy-y^2)dx+x^3dy=0 is y=(xe^{1/x})/(e^{1/x)-e^{1/x}x+c_{1}x}