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MAT252 Spring 2008

MAT252 Spring 2008. Separation of Variables. General Information. Some differential equations can be solved by the method of separation of variables (or "variables separable") . This method is only possible if we can write the differential equation in the form A(x) dx + B(y) dy = 0,

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MAT252 Spring 2008

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  1. MAT252Spring 2008 Separation of Variables

  2. General Information • Some differential equations can be solved by the method of separation of variables (or "variables separable") . This method is only possible if we can write the differential equation in the form A(x) dx + B(y) dy = 0, where A(x) is a function of x only and B(y) is a function of y only. • Once we can write it in the above form, or in a form that separates the variables one to a side, all we do is integrate throughout to obtain our general solution.

  3. Some Examples: Separation of variables can be used to solve: We can integrate this immediately:     If needed, you could solve for y explicitly. K is a constant.

  4. Solve 1. Separate the variables (a little algebra here) to get: 2. Integrate both sides: Rearrange: Another Problem

  5. One more example: Solve: Separating the variables: Some more algebra gives us: Integration by parts (left-hand side) and an easy integration on the right-hand side:

  6. NO Hints-- Solve Solution: Solve: Solution: Still have questions?? Ask in class!!

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