notes 2-2

# notes 2-2 - SECTION 2.2 SEPARABLE EQUATIONS We know how to...

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SECTION 2.2 SEPARABLE EQUATIONS We know how to solve ﬁrst order linear ordinary diﬀerential equations. What about ﬁrst order non linear ordinary diﬀerential equations? If we use x as the (independent) variable, then we want to consider dy dx = f ( x,y ) . In general we won’t know how to solve such a thing. But there are some important special cases. Separable equations. If we can do some algebra and rewrite the equation in the form S ( y ) dy dx = R ( x ) , then we can (?) just integrate both sides! Equations for which we can do this are called separable. NOTES. As always, integration may be a problem. Solving explicitly for y may also be a problem, but when we can do it, we should. Sometimes we treat

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## This note was uploaded on 05/19/2010 for the course M 427K taught by Professor Fonken during the Spring '08 term at University of Texas.

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notes 2-2 - SECTION 2.2 SEPARABLE EQUATIONS We know how to...

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