Discover the answers you need at Westonci.ca, a dynamic Q&A platform where knowledge is shared freely by a community of experts. Explore thousands of questions and answers from a knowledgeable community of experts ready to help you find solutions. Explore comprehensive solutions to your questions from knowledgeable professionals across various fields on our platform.

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

Sagot :

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.

Learn more about the differential equation here:

https://brainly.com/question/14600691

#SPJ4