How to plot implicit ODE?

How can I plot the solution of this ODE x^2.y’-y-y^2=0. Help me out please, I am new at Matlab.

Answer 1

[Davide Masiello]

You need to solve it first.

The ODE can be easily made explicit

Then you can use any Matlab ODE solver (see this documentation) to numerically solve it and then plot it using the plot function.

I suggest you give it a go, and if you stumble into problems of any sort maybe come back here and we can fix them.

[Juan Vicente]

I try to do it using ode45, but I am not getting the graph

[Davide Masiello]

First, add brackets to code the function correctly.

F = @(x,y) ((y^2+y)/x^2);

Second, the problem with you integration is that the first x value is 0.

Since x is at the denominator, this yields an array of NaN values

[x,y] = ode45(F,[0 5],0);
y

y = 41×1

0 NaN NaN NaN NaN NaN NaN NaN NaN NaN

If you start x from 1, for instance, you do get a plot.

[x,y] = ode45(F,[1 5],0);
plot(x,y)

The plot is flat because the initial value for y is also zero, which make its derivative zero too, as you can see from the ODE.

Still for the sake of example, assume that y0 = 0.1.

[x,y] = ode45(F,[1 5],0.1);
plot(x,y)

[Juan Vicente]

I get it now, but using the subjected approach, how can I plot the solution?

[Davide Masiello]

I am not sure what you mean by that, could you please clarify?

[Juan Vicente]

I got a homework to do for extra points and it is to plot the solution of that ode, I want to know if there is a way to plot it using Matlab? I attached the original graph

[Davide Masiello]

Well, if you have an analytical solution then you can just use that for plotting.

But that's a different problem, so you should change your question.

[Juan Vicente]

Thanks for the advice, I’ll do that.

[Torsten]

Solve the last equation for y and incorporate the boundary condition to get the constant C.

What's the problem ?