What is the solution for (dy)/(dx)=-(1+y^2)/(xy) ?

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

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(dy)/(dx)=-(1+y^2)/(xy)

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

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

Solution steps

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

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}

T \to 0 lim (a T + b)

f (x) = \frac{2}{2 x + 3 ^{2}}, at x = - \frac{1}{3}

\frac{d ^{2} y}{d x ^{2}} - \frac{d y}{d x} - 6 y = 10 e^{2 x} + 6 x + 7

\frac{d}{d x} (4 x^{2} + 5 x)

\int 4 x^{3} - 20 x^{2} + 8 x + 32 d x

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