# Need Help Transcribing differential equations in to Matlab code

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JB on 6 Jul 2018
Answered: Star Strider on 7 Jul 2018
I am trying to transcribe the following differential equation that describes a falling body:
dy/dt=mg/K (1-e^(-K/m t)) (with air resistance)
dy/dt=gt (without air resistance)
I would like to create a function and then call the function using ode45 and then plot a graph. I am still trying to get a good handle of matlab, but I have not been successful.

Fabricio Castro on 7 Jul 2018
Hi JB
Your problem is kind of simple to solve. With the following code you will achieve what you want:
%Supose you may want to use a time interval of [0,3] with an initial
%condition y0 equal to 50 meters
timeInterval = linspace(0,3,51);
y0 = 50;
%Defining parameters like mass (m), air resistance (K), and gravity (g)
m = 5;
K = 2;
g = 9.8;
%Using ode45 function to solve the falling body equation
[t,y] = ode45(@(t,y) (m*g)/(K*(1-exp(-K/(m*t)))), timeInterval, y0);
%Plot the result
figure
subplot(1,2,1)
plot(t,((m.*g)./(K.*(1-exp(-K./(m.*t))))),'-bo')
xlabel('time')
ylabel('dy/dt')
title('ODE graph')
set(gca,'FontSize',18)
subplot(1,2,2)
plot(t,y,'-ro')
xlabel('time')
ylabel('y')
title('Solution graph')
set(gca,'FontSize',18)
Thanks

Star Strider on 7 Jul 2018
@Fabricio Castro — We do not supply complete code to homework problems here on MATLAB Answers. The OP must demonstrate an effort. We will then help to get the posted code running.
JB on 7 Jul 2018
@Star_Strider - I appologize. Here is my first attempt at the code:
"func1.m" file: function dy = func1(t, y) dy = (m*g)/(K*(1-e^(-K/(m*t)))); end
Then calling it using ode45: [t,y] = ode45(@func1, [I have no Idea what I am doing here], y0);
I will remember to post my first attempt in my next question.
@Fabricio_Castro - Thank you for the assistance. As you can see, I am trying to create a function of the equation and then call it using ode45 and the plot the graph.
Any assistance would be greatly appreciated. I am very new to Matlab.
V/R JB

Star Strider on 7 Jul 2018
The syntax of your function is correct. However you need to spend some time with the documentation.
Specifically see the documentation on the exp (link) function.
For future reference, see the documentation on Anonymous Functions (link), and Vectorization (link).