Solve first order nonlinear ODE

Hello I am tryin to solve this nonlinear ODE

with the IC

This is my code

tspan = [0 5];
x0 = 3;
[t,x] = ode45(@(t,x) (x^4)-(7*x^2)+6*x, tspan, x0);
plot(t,x,'b')

My problem is that I get the following error: Warning: Failure at t=2.004757e-02. Unable to meet integration tolerances without reducing the step size below the smallest value allowed (5.551115e-17) at time t. What should I do because the graph of the solution looks worng. Thanks.

[J. Alex Lee]

If you have a solution form that you expect, what is it? It's not surprising that the thing explodes for x(0)>1, for which your rate of change increases to produce a snowball effect.

[Missael Hernandez]

Well is should be in the form

Wolfram doesn't give the solution Matlab does. Matlab gives this, which I think is wrong

Answer 1

[Alan Stevens]

The value of x increases far too quickly, and reaches a value beyond the numerics ability to cope with when x(0) > 2. Works just fine if x(0) = 1.5, or 0.5, say.

[Missael Hernandez]

Thank you for you explanantion!

Answer 2

[Sam Chak]

The x(t) response rises rapidly. It cannot go pass t = 0.0463782 sec.

The x(t) response diverges for x(0) > 2 and converges to some steady-state points for x(0) < 2.

tspan = [0 0.046378];
x0 = 2.5;
[t, x] = ode45(@(t,x) (x^4) - (7*x^2) + 6*x, tspan, x0);
plot(t, x, 'b')

[J. Alex Lee]

so there you go, taken together with my comment and Alan's answer, looks like you are all set.

[Missael Hernandez]

Oh ok I see. Thank you guys so much!