Linear First-Order Equations
The following is a linear first-order ODE because both
and
occur in it with power 1 and
is the highest derivative. Note that the solution contains the imaginary error function
Erfi.
| Out[1]= |  |
Here is the solution for a more general linear first-order ODE. The
variables are used as dummy variables for integration. The
Erfi term in the previous example comes from the integral in the second term of the general solution as follows.
| Out[2]= |  |
A more traditional form of the solution can be obtained by replacing
with a variable such as
.
| Out[3]= |  |
