Confused on what u do next with an exact equation, Diff EQ

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Homework Help Overview

The discussion revolves around the topic of exact differential equations, specifically focusing on verifying the exactness of a given equation and finding a corresponding function whose level curves represent the solutions. Participants are exploring the process of using mixed partial derivatives to check for exactness.

Discussion Character

  • Exploratory, Assumption checking, Mathematical reasoning

Approaches and Questions Raised

  • Participants are discussing the verification of the exactness of a differential equation through mixed partials. There are attempts to integrate expressions and check the correctness of these integrations. Questions arise regarding the integration process and the distinction between integrating and differentiating.

Discussion Status

The discussion is active, with participants providing feedback on each other's work. Some guidance has been offered regarding the integration steps, and there is acknowledgment of errors in previous attempts. Multiple interpretations of the integration process are being explored, but no explicit consensus has been reached.

Contextual Notes

Participants are working under the constraints of a homework assignment, which may limit the information they can share or the methods they can use. There is an emphasis on understanding the steps involved in determining the exactness of the differential equation.

mr_coffee
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Hello everyone. We just started working with exact equations and I'm confused on what I do next! here is the problem:
Use the "mixed partials" check to see if the following differential equation is exact.
If it is exact find a function F(x,y) whose level curves are solutions to the differential equation
http://cwcsrv11.cwc.psu.edu/webwork2_files/tmp/equations/71/5a4f0007c2fd2947228eee9825b55d1.png
http://cwcsrv11.cwc.psu.edu/webwork2_files/tmp/equations/8d/8616ca1dd6ce230911485b98a57fa31.png

Here is my work, I submitted:
2*y^2+2*x^2-4 which was wrong.

WOrk:
http://img206.imageshack.us/img206/6632/lastscan3tp.jpg

Thanks!
 
Last edited by a moderator:
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your int of 2xy^2 + 4y is incorrect
 
And what, again, is \int (2xy^2+ 4y)dx?

Did you forget that you were integrating, not differentiating?
 
Thanks everyone! yeah I don't know what i was thinking! I got:
http://cwcsrv11.cwc.psu.edu/webwork2_files/tmp/equations/8d/8616ca1dd6ce230911485b98a57fa31.png http://cwcsrv11.cwc.psu.edu/webwork2_files/tmp/equations/8b/ad397009ac98a90c5581831292c16e1.png
Which is right! weee!
 
Last edited by a moderator:

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