section%202.4

# section%202.4 - Chapter 2 First Order Dierential Equations...

This preview shows page 1. Sign up to view the full content.

Chapter 2. First Order Differential Equations § 2.4 Exact Equations 1. Def: A first order differential equation of the form M ( x, y ) dx + N ( x, y ) dy = 0 is said to be a exact equation if the expression on the left-hand side is an exact differential. And M ( x, y ) dx + N ( x, y ) dy is an exact differential iff ∂M ∂y = ∂N ∂x To solve an exact equation is to find a function f ( x, y ) such that df ( x, y ) = M ( x, y ) dx + N ( x, y ) dy , that is ∂f ∂x = M ( x, y ) ∂f ∂y = N ( x, y ) Then the solution of the equation is f ( x, y ) = C. EX: Solve the following DEs. (1) 2 xydx + ( x
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### What students are saying

• As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

Kiran Temple University Fox School of Business ‘17, Course Hero Intern

• I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

Dana University of Pennsylvania ‘17, Course Hero Intern

• The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

Jill Tulane University ‘16, Course Hero Intern