Second order differential equation graphing

I need to create this part (only helixs(?))

I created

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syms y(t)

dy = diff(y,t); d2y = diff(y,t,t);

DE = dy2 - 2*dy + 5*y == 0

cond = [y(0) ==4, dy(0) == 0]

sol = dsolve(DE, cond)

y = matlabfunction(sol)

dy1 = matlabfunction(diff(y,t))

x = linspace(-6, 6, 250);

plot(y(x),dy1(x), 'blue', 'LineWidth',3)

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This code created

How should I create multiple of lines?

instead of just one line?

Answer 1

[Stephan]

Hi,

to get different plots you need to change the initial conditions - try this:

clear all
close all
clc
syms y(t) dy(t)
eqn = diff(y,t,2) - 2*diff(y,t) + 5*y == 0;
dy(t) = diff(y,t);
%cond = [y(0) ==4 , dy(0) == 0];
sol_y = dsolve(eqn)
sol_Dy = diff(sol_y,t);
odefun = matlabFunction([sol_y; sol_Dy],'Vars',{'t','C1','C2'});

t = linspace(-6,6,250);
hold on
for k = -4:1:4
    res = (odefun(t,k,k/2))';
    if mod(k,2) == 0
        plot(res(:,1),res(:,2),'b', 'LineWidth',2)
    elseif mod(k,2) == 1
        plot(res(:,1),res(:,2),'r', 'LineWidth',2)
    end
end
xlim([-5 5]);
ylim([-5 5]);
hold off

Usually the commands:

clear all
close all

are not recommended - but since you need C1 and C2 to be named exactly like this i did this, to ensure the constants get correct names. Else they would possibly be named C3 and C4 and the code would not work properly.

If you divide the part of create the function handle from calculate values and plot, you can solve this easily. The first part of the code doesnt need to be computed every time. Just save the function handle to a .m-file and you can use only the second part of the code.

Result is:

.

Best regards

Stephan