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

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

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

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

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

Solution steps

(y^{2} + 1) 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}

(2 a^{2} - r^{2}) d r = r^{3} sin (θ) d θ

y^{^{'}} - \frac{y}{x} - 1 = \frac{1}{x} + y

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

\frac{d y}{d t} + 2 y = 0, y (0) = 3

\frac{d y}{d x} + 6 x^{2} y = 5 x^{2}, y (0) = 4

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