## 17Calculus Partial Differential Equations - Solve With Direct Integration

##### 17Calculus

Direct Integration Solution

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 $$u_{xx} = 1$$.

### Michel vanBiezen - General Sol. of 2nd Order PDE

video by Michel vanBiezen

This same technique extends to higher dimensions as well.  Here is an example.

Example 2

Find $$u(x,y,z)$$ that solves $$u_{xx} = 1$$.

### Michel vanBiezen - General Sol. of PDE w/ 3 Variable

video by Michel vanBiezen

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