What is the solution for x*y*y^'=1-x^2 ?

The solution for x*y*y^'=1-x^2 is y=sqrt(2ln(x)-x^2+c_{1)},y=-sqrt(2ln(x)-x^2+c_{1)}

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xyy^'=1-x^2

x \cdot y \cdot y^{^{'}} = 1 - x^{2}

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

Solution steps

x \cdot y \cdot y^{'} (x) = 1 - x^{2}

Solve separable ODE:

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

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

\frac{d}{d x} (\frac{x ^{3} - x}{x})

\frac{d}{d x} (\frac{4}{( x ^{3} + 9 ) ^{5}})

\frac{d x}{d t} + 2 t^{5} x^{7} + \frac{x}{t} = 0

n = 0 \sum \infty e^{- 6 n}

(7, - 4), (8, 8)

What is the solution for x*y*y^'=1-x^2 ?
The solution for x*y*y^'=1-x^2 is y=sqrt(2ln(x)-x^2+c_{1)},y=-sqrt(2ln(x)-x^2+c_{1)}