The differential equation [tex]cos(x)dx+\frac{y}{x} dy=0[/tex] is not exact.
For given question,
we have been given a differential equation [tex]cos(x)dx+\frac{y}{x} dy=0[/tex]
We have to determine given differential equation is exact or not.
Compare it with M dx + N dy = 0
⇒ M = cos(x) and N = y/x
Find the derivative of M with respect to y.
[tex]\Rightarrow M_y=-sin(x)[/tex]
Now, find the derivative of N with respect to x.
[tex]\Rightarrow N_x=\frac{-y}{x^{2} }[/tex]
Since [tex]M_y \neq N_x[/tex], given differential equation is not exact.
Therefore, the differential equation [tex]cos(x)dx+\frac{y}{x} dy=0[/tex] is not exact.
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