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

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

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(dy)/(dx)=(x(1-y))/(x^2-2)

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

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

Solution steps

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

Solve separable ODE:

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

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

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