TUT0702 Quiz2

[Qihui Huang]

Determine whether the equation is exact or not

$$(e^xsin(y)-2ysin(x))-(3x-e^xsin(y))y'=0$$
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.

[Zhangxinbei]

Hi Qihui! Same as you until My ?= Nx
I tried My-Nx/M, My-Nx/N and Nx-My/XM-YN, 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