Question

Verify whether the given differential equation is exact or not. if exact, solve. cosx y/x dx dy

Answer 1

The differential equation $cos(x)dx+\frac{y}{x} dy=0$ is not exact.

For given question,

we have been given  a differential equation $cos(x)dx+\frac{y}{x} dy=0$

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.

$\Rightarrow M_y=-sin(x)$

Now, find the derivative of N with respect to x.

$\Rightarrow N_x=\frac{-y}{x^{2} }$

Since $M_y \neq N_x$, given differential equation is not exact.

Therefore, the differential equation $cos(x)dx+\frac{y}{x} dy=0$ is not exact.

Learn more about the differential equation here:

brainly.com/question/14600691

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