Hey guys, I have a question concerning the rewriting of a differential equation solution.(adsbygoogle = window.adsbygoogle || []).push({});

In the example above, they rewrite [y=(plus/minus)e^c*sqrt(x^2+4)] as [y=C*sqrt(x^2+4)]. I understand that the general solution we get as a result represents all the possible functions, but if we were to attempt to find a particular solution given an initial condition (a point on the graph of the equation), I would think that we would plug in the coordinate into not the general solution but the one above it with the (plus/minus). The problem is that in some of the problems that is not the case - you plug in the coordinate into the general solution to find your equation.

The reason I would plug in the coordinate into the (plus/minus) equation is because that is the original equation contains above the x-axis values and below the x-axis values (when you graph the resulting equation). But if you plug a coordinate into the general solution, you only get the top portion of bottom portion of the graph depending on if y were less than or greater than 0 (because of the absolute value symbol). So plugging into the general solution kind of makes you lose a portion of the equation's graph.

Hopefully you guys can help clear up this confusion for me. If you need any clarification, please ask.

Thanks!

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# Integrating differential equations that have ln

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