What is the solution for xdx+ydy=xy(xdy+ydx) ?

The solution for xdx+ydy=xy(xdy+ydx) is y=sqrt((c_{1)+x^2-1)/(x^2-1)},y=-sqrt((c_{1)+x^2-1)/(x^2-1)}

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xdx+ydy=xy(xdy+ydx)

x d x + y d y = x y (x d y + y d x)

y = \frac{c _{1} + x ^{2} - 1}{x ^{2} - 1}, y = - \frac{c _{1} + x ^{2} - 1}{x ^{2} - 1}

Solution steps

x d x + y d y = x y (x d y + y d x)

Solve separable ODE:

y = \frac{c _{1} + x ^{2} - 1}{x ^{2} - 1}, y = - \frac{c _{1} + x ^{2} - 1}{x ^{2} - 1}

y = \frac{c _{1} + x ^{2} - 1}{x ^{2} - 1}, y = - \frac{c _{1} + x ^{2} - 1}{x ^{2} - 1}

y^{^{'}} \cdot ln (y) - y = 0

\frac{x ^{2}}{y} - 4 x e^{y^{2}} \frac{d y}{d x} = 0

y^{^{'}} = \frac{( x ^{2} - 5 )}{y ^{2}}, y (0) = 3

x^{^{'}} = b^{2} + x

\frac{d y}{d x} = 0.04 - \frac{3 y}{880}

What is the solution for xdx+ydy=xy(xdy+ydx) ?
The solution for xdx+ydy=xy(xdy+ydx) is y=sqrt((c_{1)+x^2-1)/(x^2-1)},y=-sqrt((c_{1)+x^2-1)/(x^2-1)}