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So I have the following differential equation: $$ \frac{dy}{dt}-0.07y=5000 $$ I tried solving it using an integrating factor and ended up getting $y=Ce^{0.07t}-350$. I plugged the ODE into Wolfram Alpha and it seemed to solve the problem as a separable equation. obtaining the result: $Ce^{0.07t}-71428.6$. Have I made a mistake in choosing to solve the equation with an integrating factor and if I am mistaken than when am I allowed to use this method and why not in this case?

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  • $\begingroup$ Also I am unsure how I can put the math in my questions into a more readable format. I have looked into mathjax but I'm not sure what to do after unzipping it. $\endgroup$ – TQM Jul 20 '13 at 0:44
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Any linear first order differential equation can be solve using an integrating factor. As this is indeed linear and first order, you are certainly on the right track.

Your error was multiplying 5000 by 0.07. Indeed, this is exactly what you would do if you were to differentiate $5000e^{-0.07t}$. However, in using the integrating factor method, you are instead supposed to integrate this term.

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  • $\begingroup$ Wow, very stupid mistake. Thanks. I wish there was a way for me to delete this question now. How embarrassing. $\endgroup$ – TQM Jul 20 '13 at 0:51
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    $\begingroup$ I've made that mistake in teaching a differential equations class. It happens. $\endgroup$ – RghtHndSd Jul 20 '13 at 0:51

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