# Numerical And Graphical Solutions To Odes; Numerical Solution Of First-order Ode - HP 49g+ User Manual

Graphing calculator.

0 HERMITE, result: 1,
1 HERMITE, result: '2*X',
2 HERMITE, result: '4*X^2-2',
3 HERMITE, result: '8*X^3-12*X',

## Numerical and graphical solutions to ODEs

Differential equations that cannot be solved analytically can be solved
numerically or graphically as illustrated below.

### Numerical solution of first-order ODE

Through the use of the numerical solver (‚Ï), you can access an input
form that lets you solve first-order, linear ordinary differential equations.
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
1/2
v
, 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: ‚Ï˜ @@@OK@@@ . Enter the following parameters:
*
i.e., H
= 1.
0
*
i.e., H
= 2x.
1
*
2
i.e., H
= 4x
-2.
2
*
3
i.e., H
= 8x
-12x.
3
The
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