Mat252 spring 2008
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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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Mat252 spring 2008

MAT252Spring 2008

Separation of Variables


General information

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.


Some examples

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.


Another problem

Solve

1. Separate the variables (a little algebra here) to get:

2. Integrate both sides:

Rearrange:

Another Problem


One more example

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:


No hints

NO Hints--

Solve

Solution:

Solve:

Solution:

Still have questions?? Ask in class!!


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