Direct Integration Solution
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The first technique you should always try to solve partial differentiation is direct integration.  Direct Integration can be used similarly to separation of variables for ODE's.  If there is just one partial derivative term with no coefficient and all other terms can be moved to the other side of the equal sign, then direct integration may be possible.
Let's look at an example.
Example 1
Find \(u(x,y)\) that solves \(u_{xx} = 1\).
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This same technique extends to higher dimensions as well.  Here is an example.
Example 2
Find \(u(x,y,z)\) that solves \(u_{xx} = 1\).
video by Michel vanBiezen |
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Really UNDERSTAND Differential Equations
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