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

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