Question

Examine whether the given differential equation is exact or not:

$ydx-xdy=0$.

Answer 1

Given the differential equation is $ydx-xdy=0$........(1)

Comparing this with $Mdx+Ndy=0$.....(2) we have,

$M=y$ and $N=-x$.

Now $M_y=1$ and $N_x=-1$.

We have the differential equation (2) will be exact when $M_y=N_x$.

But for the equation (1) we don't have $M_y=N_x$, so the given differential equation (1) is not exact.