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First Course in Differential Equations

by: Angelina Bauch

First Course in Differential Equations MATH 383

Marketplace > University of North Carolina - Chapel Hill > Mathematics (M) > MATH 383 > First Course in Differential Equations
Angelina Bauch
GPA 3.89


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This 2 page Study Guide was uploaded by Angelina Bauch on Sunday October 25, 2015. The Study Guide belongs to MATH 383 at University of North Carolina - Chapel Hill taught by Staff in Fall. Since its upload, it has received 74 views. For similar materials see /class/228752/math-383-university-of-north-carolina-chapel-hill in Mathematics (M) at University of North Carolina - Chapel Hill.

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Date Created: 10/25/15
Math 302 Differential Equations Metcalfe Summer 2001 June 1 2001 Solving Exact Differential Equations Section 26 When Use this technique for rst order exact equations If you write your rst order ordinary differential equation in the form M7ydN7ydy0 then it is exact if 8M 8N EE i i i i i 3 3 dy What We want to nd a function m y whose derivative total derivative 8 8 d is 13 13 d Mm y Nzyd y Once we have such an 1 setting m y c for a constant c will give us a solution to our differential equation How 0 Check that your differential equation is rst order o Rewrite the differential equation in the form M7ydNm7ydy 0 0 Check exactness My N1 0 We want to nd an function m y so that fmzy Mm y so integrate awmem Here the constant of integration will be a function of y c We also want 1 to satisfy fyz y Nzy so differentiate the result of the previous step with respect to y and set it equal to Nz Use this to resolve the integration constant Plug the integration constant in so that you have a function fzy whose total derivative is as desired Then to get a solution set m y c for a constant c o If given use an initial conditions to resolve this 0 Check your solution by taking the derivatives and comparing it to the original equation


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