Linear First-Order Equations

The following is a linear first-order ODE because both y[x] and y[x] occur in it with power 1 and y[x] is the highest derivative. Note that the solution contains the imaginary error function Erfi.

Here is the solution for a more general linear first-order ODE. The K 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.

A more traditional form of the solution can be obtained by replacing K[1] with a variable such as t.