Exact & non differential equation - SlideShare
www.slideshare.net › SIDDHI31 › exact-nonAug 02, 2015 · Example : 3 Solve π¦4 + 2y dx + π₯π¦3 + 2π¦4 − 4π₯ ππ¦=0 Solution: Here M=π¦4 + 2π¦ and so ππ ππ¦ = 4π¦3+2 N=π₯π¦3 + 2π¦4 − 4π₯ and so ππ ππ₯ = π¦3 − 4 Thus, ππ ππ ≠ ππ ππ₯ and so the given differential equation is non exact. 188/2/2015 Differential Equation
Lecture 04 Simplest Non-Exact Equations
www.math.ualberta.ca › ~xinweiyu › 334Finally the solution to the initial value problem is exy cos2 x − 3 y+ x2 = e21 cos6 − 12. (21) Linear equations. Fortunately there are many important equations that are exact, unfortunately there are many more that are not. • The simplest non-exact equation. y′ = y or equivalently −y dx +dy=0. (22) We easily check ∂M ∂y = −1 0= ∂N ∂x. (23)