Solving a second order differential equation

Hello everyone,

I have the differential equation ? 2? ?? 2 + 10 ?? ?? + 16? = 16 ;

I need to solve the equation using ode45 with the inital values of y=0 and dy_dt = 0. I have a time interval of t= 0 to 8.63644. But apparently the script also has to find the maximum values of y and dy_dt with corresponding time t. I managed to wrote 2 seperate scripts for it which are my maincode function and seperate equation function.

So for the main code I have;

clear all

time_interval = [0 215911/25000];

initial = [0 0];

[t,y] = ode45(@Q5, time_interval, initial);

plot(t,y(:,1)), title('y vs t')

figure

plot(t, y(:,2)), title('dy_dt vs t')

And for the equation script, I have;

function results = Q5(t,y)

results = [y(2);10*y(2)-(16*y)+16];

But I keep getting these specific errors:

Error using odearguments (line 95)

Q5 returns a vector of length 3, but the length of initial conditions vector is 2. The vector returned by Q5 and the initial conditions vector must have the same number of

elements.

Error in ode45 (line 115)

odearguments(FcnHandlesUsed, solver_name, ode, tspan, y0, options, varargin);

Error in Q5_maincode (line 7)

[t,y] = ode45(@Q5, time_interval, initial);

I have tried using size function to equate to arrays but it did not work.

My inquiry is that which functions should I use to rectify the errors? Or how do I fix the errors so to say. Any help would be appreciated, thanks in advance.

Version: 9.6

Answer 1

[J. Alex Lee]

In you function Q5, your 2nd row has a typo, using y instead of y(1)