Page 16-57 of the HP-50G User's Guide covers this...

"Numerical solution of first-order ODE

Through the use of the numerical solver (RS-NUM.SLV), you can access an input

form that lets you solve first-order, linear ordinary differential equations. The

use of this feature is presented using the following example.The method used

in the solution is a fourth-order Runge-Kutta algorithm preprogrammed in the

calculator.

Example 1 -- Suppose we want to solve the differential equation, dv/dt = -1.5

v1/2, with v = 4 at t = 0. We are asked to find v for t = 2.

First, create the expression defining the derivative and store it into variable EQ.

The figure to the left shows the ALG mode command, while the right-hand side

figure shows the RPN stack before pressing K.

Then, enter the NUMERICAL SOLVER environment and select the differential

equation solver ... Etc." (Emphasis mine)