## 40 Reputation

0 years, 285 days

## general solution of ODE...

Maple

solve it by Maple , get the following form solution, what's the Int(1,0)

 > restart;

 > ODE :=diff(r(t),t)=r(t)*(1-r(t)^2)+mu*r(t)*cos(t)
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## The phase portrait of ode system...

How can I  get the  phase portrait  and several trajectory of the following system(it is in polar coordinates )

r'=r(1 − r^2) + 2rcos(θ),

θ' = 1

## dimensionless ODE model...

Maple

For the following system, the parameters D_1,D_2,D_3,D_4,D_5,D_6,S are all positive, How can I get all the  equilibrium  and their stability.

diff(x1,t)=fS;diff(x2,t)=fV;diff(x3,t)=fC;diff(x4,t)=fR;

fS := -D2*x1*x2-D1*x1-x1*x3+S; fV := D2*x1*x2-D4*x2+x1*x3; fC := -D6*x3*x4-D5*x3+x2; fR := D6*x3*x4-x4

## Numerical solution of Non-autonomous ODE...

Maple

How can I use maple to get the numerical solution of this non-autonomous system

sys_ode := diff(x(t), t) = ax(t)-bx(t)y(t)+2sin(t), diff(y(t), t) = -cy(t)+dx(t)y(t)

where a,b,c,d is parameters, they can take any value.

## problem with ode ...

Maple

why is  the figure  so weird ? How can I get the smooth trajectories of the ode system?

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 \left[ \begin {array}{cc} -2&0\\ \noalign{\medskip}0&0\end {array}  \right]

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