# Thread: phase portrait for ODE

1. ## phase portrait for ODE

iv been given an ode

dx/dt = x^4 + 4*(x^3) - 60*(x^2)

i want to sketch the phase porrait for this ODE...does any have any ideas or can show me how to what to do thankz

2. Originally Posted by dopi
iv been given an ode

dx/dt = x^4 + 4*(x^3) - 60*(x^2)

i want to sketch the phase porrait for this ODE...does any have any ideas or can show me how to what to do thankz
The general solution is,
$\frac{1}{5}x^5+x^4-20x^3+C$
The curves are represented below.
(There is more to the curves, it just happens to be far away).

3. ## asymptotic behaviour

have the ode

dx/dt = x^4 +4(x^3) - 60(x^2)

generally the solution s x(t) satisfy x(0) = x[0]

and i found out that the
attactor is -10
repellor is 6
and 0 is niether

however i want to describe the asymptotic behaviour of the solution satisfying x(0) = 1/2 , which is were i got stuck??