Difference between revisions of "Solutions of Differential Equations"

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(Created page with "A solution of a differential equation is an expression of the dependent variable that satisfies the relation established in the differential equation. For example, the solutio...")
 
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==Resources==
 
==Resources==
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* [http://www.maths.gla.ac.uk/~cc/2x/2005_2xnotes/2x_chap5.pdf Differential Equations],

Revision as of 19:30, 17 September 2021

A solution of a differential equation is an expression of the dependent variable that satisfies the relation established in the differential equation. For example, the solution of will be some equation y = f(x) such that y and its first derivative, y', satisfy the relation . The general solution of a differential equation will have one or more arbitrary constants, depending on the order of the original differential equation (the solution of a first order diff. eq. will have one arbitrary constant, a second order one will have two, etc.).

Examples:

  • . Through simple integration, we can calculate the general solution of this equation to be , where C is an arbitrary constant.
  • . The G.S. is . , so , so this solution satisfies the relationship for all arbitrary constants C.
  • . The G.S. is . , so becomes .


Resources