What is an exact differential equation?

There must be a 0 on the right side of the equation and and must be separated by a +.

__Steps to solve exact differential equations:__- Verify that
- Find and
- Integrate or
- This will help us find
- Replace c with if you integrated with respect to y, or if you integrated with respect to x
- Compute or
- Solve to get the implicit or explicit solution, depending on which is preferred
- Don’t forget to substitute or

__First example (click here):__1. Verify that

2. Integrate

3. Replace c with

4. Compute

We took the derivative with respect to x of , which is equal to . We then compared the derivative to , the equation we didn’t integrate. We then integrated both sides to solve for .

5. Find the implicit equation

__Here’s another example (click here):__Exact differential equations may look scary because of the odd looking symbols and multiple steps. If you double check your work, memorize the steps, and practice, you can definitely get this concept down. Don’t be afraid and dive in!

Until next time,

Leah

Find the function u(u,t), define for 0<x<π and t≥0, which satisfies the following condition:

ReplyDeletedu/dt=(d^2 u)/〖dx〗^2 u(θ,t)=u(π,t)=0

u(x,0)=sinx+3sin2x-5sin3x

Thanks. This is a good help to those students who afraid to differential equations. But I think that the way it can be memorized should be applications of differential equatons.

ReplyDeleteThis is really interesting but i need urgent solution to this questions

ReplyDelete1. solve d^2y/dx^2-4dy/dx+4y=8(x^2+e^2x)

2. determine the regular singular point of the differential equation 2x(x-1)y"+3(x+1)y'-y=0