ploting differential equation 2 order

hello, i'm new and i can't solve this second order deffirential equation : -y'=y''+3y+cos(wt) where w=0.1,1,10 and t=[0;100] and after that plot the equation with 3 different plot on the same graph

    y0=[0 0]
  w=0.1
  tspan=[0,100]
  odefun=@(t,y) [y(2);cos(w*t)+y(2)+3*y(1)];
  [t,y]=ode45(odefun,tspan,y0);
  plot(t,y)

I do this but i'm not sure if it's true or false. Thank you for your help.

Answer 1

[Jim Riggs]

Here is how to do this:

 y0=[0 0]
 tspan=[0,100]

 w=0.1
 odefun=@(t,y) [y(2);cos(w*t)+y(2)+3*y(1)];
 [t1,y1]=ode45(odefun,tspan,y0);

 w=1.0
 odefun=@(t,y) [y(2);cos(w*t)+y(2)+3*y(1)];
 [t2,y2]=ode45(odefun,tspan,y0);

 w=10.0
 odefun=@(t,y) [y(2);cos(w*t)+y(2)+3*y(1)];
 [t3,y3]=ode45(odefun,tspan,y0);

Now you have three solutions, t1,y1, t2,y2, and t3,y3 for values of w=0.1, 1.0 and 10.0.

When you define an anonymous function using a constant (in this case w) the constant becomes embedded in the function. That's why you have to re-define the function when you change the value of w.

Note that y1, y2, and y3 contain two columns each. You can plot these using:

figure;
plot(t1,y1(:,1),'r');
hold on;
grid on;
plot(t2,y2(:,1),'b');
plot(t3,y3(:,1),'g');
legend('w=0.1','w=1.0','w=10.0');

The notation y1(:,1) y2(:,1) y3(:,1) indicates the first column. If you want to plot the second column, change the 1 to a 2.