Need example of real application of differential equation

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I'm teaching Calculus and am looking for an example of a first order differential equation application that is reasonably easy to explain in terms of where the equation comes from, but difficult or impossible to solve.

I'm trying to show when you would need to use approximation techniques like Euler's method. All the book examples are differential equations with solutions so my students are having a hard time seeing why they need to bother to learn slope fields and approximations of solutions.

Any help would be greatly appreciated.
B. Gallis
 

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chiro
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I'm teaching Calculus and am looking for an example of a first order differential equation application that is reasonably easy to explain in terms of where the equation comes from, but difficult or impossible to solve.

I'm trying to show when you would need to use approximation techniques like Euler's method. All the book examples are differential equations with solutions so my students are having a hard time seeing why they need to bother to learn slope fields and approximations of solutions.

Any help would be greatly appreciated.
B. Gallis
Typically the harder DE's to solve are the ones that are non-linear in some form.

All the 'linear' type DE's typically have an algorithmic method to find their solution.

Unfortunately in my education most of the examples that were used were linear and pretty straightforward since most of them fell into some category.

My solution is that if you want to entice the students to learn about numerical or approximate methods, then use a non-linear example with no analytic solution. Some problems with heating and cooling may have these, but i'm sure there are many examples in books or on the internet that exist.
 

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