Explicit Solution

   Explicit solution is a solution where the dependent variable can be separated.

An explicit solution is any solution that is given in the form .  In other words, the only place that y actually shows up is once on the left side and only raised to the first power.


EXAMPLE

  Find an actual explicit solution to .

Solution We already know from the previous example that an implicit solution to this IVP is .  To find the explicit solution all we need to do is solve for .

                                                            

Now, we’ve got a problem here.  There are two functions here and we only want one and in fact only one will be correct!  We can determine the correct function by reapplying the initial condition.  Only one of them will satisfy the initial condition.

In this case we can see that the “-“ solution will be the correct one.  The actual explicit solution is then