What is the solution for (1+y^2)dx+xydy=0 ?

The solution for (1+y^2)dx+xydy=0 is y=(sqrt(c_{1)-x^2})/x ,y=-(sqrt(c_{1)-x^2})/x

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(1+y^2)dx+xydy=0

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

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

Solution steps

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

Solve separable ODE:

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

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

x = \frac{7}{y}, x = \frac{y}{9}, x = 9 y

x \to 0 lim (2 x cot (x))

\frac{d}{d x} (\frac{( 2 x + x ^{2} )}{( 1 + x ) ^{2}})

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

ln (3 - 2 x)

What is the solution for (1+y^2)dx+xydy=0 ?
The solution for (1+y^2)dx+xydy=0 is y=(sqrt(c_{1)-x^2})/x ,y=-(sqrt(c_{1)-x^2})/x