MATLAB: Plotting second order ode response

Control System Toolboxdifferential equations

I have been trying to plot the curve of 'y', the step response of a differential equation but my code doesn't seem to work, please help.

clear all, close all, clc
y = dsolve('D2y+12*Dy+36*y=36', 'y(0) = 0','Dy(0) = 0')
pretty(y)

Best Answer

f=matlabFunction(y);
t=0:.001:1;
plot(t,f(t)),grid

If you have the Control System Toolbox:

step(tf(36,[1 12 36]))

Related Solutions

MATLAB: How do i solve a second order ODE with variable coefficients

This seems to work:

% % % y''+(exp(-10t)+sen(10t))y'+y = 0
syms t y(t) Y
D1y = diff(y,t);
D2y = diff(y,t,2);
Eqn = D2y + exp(-10*t) + sin(10*t)*D1y + y == 0;
yode = odeToVectorField(Eqn);
Yodefcn = matlabFunction(yode, 'Vars',[t Y]);
% Yodefcn = @(t,Y) [Y(2);-exp(t.*-1.0e1)-sin(t.*1.0e1).*Y(2)-Y(1)];
tspan = [0 15];
Y0 = [0 0];
[T,Y] = ode45(Yodefcn, tspan, Y0);
figure(1)
plot(T, Y)
grid

If you do not have the Symbolic Math Toolbox, delete that part of my code and use the commented ‘Yodefcn’ instead, with the rest of my code.

MATLAB: Solve a second order differential equation in matlab

You can transform your equation d2y/dx2=.-5dy/dx-7y to get:

y1=y
y2=dy/dx
dy1=dy/dx=y2
dy2=d2y/d2x=-5dy/dx-7y=-5y2-7y1

Create a file named myode.m

function dy=myode(x,y)
dy=[0;0]
dy(1)=y(2)
dy(2)=-5*y(2)-7*y(1)

Then run these lines

yin=[0 4 ]  % initial values
time=[0 5]
[x,y]=ode45(@myode,time,yin)
plot(x,y)

Best Answer

Related Solutions

MATLAB: How do i solve a second order ODE with variable coefficients

MATLAB: Solve a second order differential equation in matlab

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