What is the solution for xydy=(1+y^2)(1-x)dx ?

The solution for xydy=(1+y^2)(1-x)dx is y=sqrt(e^{-2x+c_{1)}x^2-1},y=-sqrt(e^{-2x+c_{1)}x^2-1}

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xydy=(1+y^2)(1-x)dx

x y d y = (1 + y^{2}) (1 - x) d x

y = e^{- 2 x + c_{1}} x^{2} - 1, y = - e^{- 2 x + c_{1}} x^{2} - 1

Solution steps

x y d y = (1 + y^{2}) (1 - x) d x

Solve separable ODE:

y = e^{- 2 x + c_{1}} x^{2} - 1, y = - e^{- 2 x + c_{1}} x^{2} - 1

y = e^{- 2 x + c_{1}} x^{2} - 1, y = - e^{- 2 x + c_{1}} x^{2} - 1

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

\frac{d}{d t} (H (t)) = 4 - 0.5 H (t), H (0) = 0

\frac{d y}{d x} = \frac{10 + 16 x}{x y ^{2}}, y = 4, x = 1

y^{2} + y - x \frac{d y}{d x} = 0

y d x + (x - 6) d y = 0

What is the solution for xydy=(1+y^2)(1-x)dx ?
The solution for xydy=(1+y^2)(1-x)dx is y=sqrt(e^{-2x+c_{1)}x^2-1},y=-sqrt(e^{-2x+c_{1)}x^2-1}