Toronto Math Forum
MAT2442019F => MAT244Test & Quizzes => Quiz2 => Topic started by: Qihui Huang on October 04, 2019, 02:12:37 PM

Determine whether the equation is exact or not
$$(e^xsin(y)2ysin(x))(3xe^xsin(y))y'=0$$
Let $$M(x,y)=e^xsin(y)2ysin(x)$$ and let $$N(x,y)=3x+e^xsin(y)$$
Then, $$M_y(x,y)=e^xcos(y)2sin(x)$$ $$N_x(x,y)=3+e^xsin(y)$$
Since $$M_y \neq N_x$$
so the given differential equation is not exact.

Hi Qihui! Same as you until My ?= Nx
I tried MyNx/M, MyNx/N and NxMy/XMYN, all wrong. Did he said we don't need to count it? Just to show that the equation not exact should be fine, right?
Thank you