Question: Numerical solution for the system of nonhomogenous ODE with conditions.


I need help for the following. I have system of ODE as follows



eq1 := diff(a[1](t), t)-.2752730484*(diff(a0(t), t))-.4613755069*(diff(theta(t), t))*a0(t)+.5076391815*a[1](t)+.4613755069*(diff(theta(t), t))*a[1](t)-.5076391815*a0(t)-.2699348119-3.101092194*(diff(theta(t), t))*a[2](t)-3.412049143*a[2](t):

eq2 := diff(a[2](t), t)+1.974216606*(diff(theta(t), t))*a[2](t)+2.172177949*a[2](t)+.8118640378*(diff(a0(t), t))-.5168486990*(diff(theta(t), t))*a0(t)+.5686748572*a[1](t)+.5168486990*(diff(theta(t), t))*a[1](t)-.5686748572*a0(t)-.3023902529:

eq3 := diff(x(t), t, t)+0.3162815552e-1*(diff(x(t), t))+2.500850554*x(t)+55.56175404*d-9.404372784*Pi:

eq4 := diff(theta(t), t, t)+0.2e-1*(diff(theta(t), t))+theta(t)+2.685034823+4*d-.6770393014*Pi:

# I need to solve above system of ode for a[1](t), a[2](t) and x(t) and theta(t) numerically using rkf45 (i only know about solving equations numerically in maple without any condition) with conditions as when -x(t) < a[1](t), d will be x(t)+a[1](t) in eq3 and eq4 and a0(t) is replaced by -x(t) in eq1 eq2 otherwise d will be 0 in equation3 and 4 and a0(t) will be a[1](t). Initial conidtion for these are a[1](0)=0.29, D(x)(0)=.1362, x(0)=0, theta(0)=10, D(theta)(t)=0.366. I also have to make a bifurcation diagram for above system of equations. Please help me.


Please help me for this.





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