Differential equation question Solve the following differential equation $(1+xy)ydx + (1-xy)xdy=0$.
I have been taught to solve differential equations of the following type:
1.Homogeneous
2.Variable separable
3.Linear differential equation
But, I'm unable to find to which category the given differential equation belongs.Please help. I would like some hints towards solving the question and please don't post the answer.
Set $\xi = xy$, $\eta = \frac{x}{y}$. Then
$$\begin{align}
\mathrm{d}\xi &amp;= y\,\mathrm{d}x + x\,\mathrm{d}y
&amp; \mathrm{d}\eta &amp;= \frac{y\,\mathrm{d}x - x\,\mathrm{d}y}{y^2}
\end{align}$$
And therefore
$$\mathrm{d}\xi + \frac{\xi^2}{\eta}\mathrm{d}\eta = 0$$
I suppose, you can take it from there.
IF you have anything of form f(x.y)y dx + g(x.y)x dy = 0 ; then I.F. will be 1/(Mx-Ny) . Multiply this to make it exact differential equation.