# First order differential equation solver with Ti-84 plus

## Get insight into the numeric differential equation solver for your Ti-84

A very powerful Ti-84 Basic Program is the first order Differential Equation Solver. The program DV1ETRP3.8xp solves the first order linear differential equation. A useful program for electrical engineers to solve transient problems in RC and RL circuits. The basic equation is shown below. The program is demonstrated for a constant f(x)=0.6, a=0.1, b=0.7.

The analytical solution is given by the formula:

With the analytical solution, we check how accurate the results of the program DV1ETRP3 program approaches the analytical solution,

To run the Program DV1TRP3, follow the next steps:

1: Start the program DV1ETRP3 from the menu.

2: Enter the step size dx which determines the accuracy of the results. A smaller step size gives better results but takes more processor time. As rule of thumb, we take dx=(a/10b). (a/b) is also called the time constant τ (say tau) of a system. More information about step size choice is available on the page:

3: Xmax is the maximum X in which area Y is solved. We take 5 times the time constant = 5*0.1/0.7

4: Y(0) is the initial value of Y. In this case, we take Y(0)= 0. (The initial value depends on the history of the process.)

5: a=0.1, b=0.7

6: To define f(x) there are 2 possibilities: direct (in our case f(x)=0.6) or by a special input already generated with the program Funcgen, Funcst1 or PWM.

8: Now the program is ready to solve the problem. All the steps and the results are shown here below. By default, only the output signal is shown, but you can view the input signal too by activating Y6.

To validate the numerically calculated results against the analytical solution, both sets of data are compared at the specific x-value of x=0.32857. At this x-value, the numerical result is 0.77137.

The analytical result is 0.77117

The difference between the two solutions is 0.77117 - 0.77137 = 0.00020, which is a deviation of less than 1%.

A more precise numerical result can be achieved by reducing the step size by a factor of 5. With this adjusted step size, the numerical and analytical results converge.

Calculation time Ti-84 Plus CE=14 sec.

Calculation time Ti-84 Plus =45 sec.

The CE version is more than 3 times faster

The program DV1ETRP3 can store up to 1000 calculated steps. Further information about steps and the concept of a step is available at:

Additional examples of the DV1ETRP3.8xp program, demonstrating its usage with various input functions, can be found on YouTube.

News July 2023: The third version DV1ETRP3 is now available, featuring the capability to store 999 calculated points. If you have any inquiries or would like to request the program, kindly contact us at ti84.org@gmail.com , and we will promptly send you the program. Please remember to include your email address in your correspondence!