# Question:Trouble with some differential equations

## Question:Trouble with some differential equations

Maple

I'm attempting to solve a big set of diff eqs.  I've heard maple has trouble with complex differential equations so I've broken them up into the real and imaginary parts.

The equations are as follows:

eq1 := diff(RBx(x, t), t) = -x*IBx(x, t)-IUx(x, t)
eq2 := diff(IBx(x, t), t) = x*RBx(x, t)+RUx(x, t)
eq3 := diff(RBy(x, t), t) = -x*IBy(x, t)-IUy(x, t)-3*RBx(x, t)/(2*omega)
eq4 := diff(IBy(x, t), t) = x*RBy(x, t)+RUy(x, t)-3*IBx(x, t)/(2*omega)
eq5 := diff(RBz(x, t), t) = -x*IBz(x, t)-IUz(x, t)eq6 := diff(IBz(x, t), t) = x*RBz(x, t)+RUz(x, t)
eq7 := diff(IUx(x, t), t) = -x*IUx(x, t)-IBx(x, t)+2*RUy(x, t)/omega
eq8 := diff(RUx(x, t), t) = x*RUx(x, t)+RBx(x, t)+2*IUy(x, t)/omega
eq9 := diff(RUy(x, t), t) = -x*IUx(x, t)-IBx(x, t)-RUx(x, t)/(2*omega)
eq10 := diff(IUy(x, t), t) = x*RUx(x, t)+RBx(x, t)-IUx(x, t)/(2*omega)
eq11 := diff(RUz(x, t), t) = -x*IUx(x, t)-IBx(x, t)
eq12 := diff(IUz(x, t), t) = x*RUx(x, t)+RBx(x, t)

My initial conditions are everything is zero and RBx(x,o)=exp(-x^2/(2*sigma^2)) and RBz(x,0)=diff(RBx(x,o),x)

Here sigma is defined so that the FWHM is 20 or sigma := 20/(2*sqrt(2*ln(2))).  Omega is a parameter that I hope to set later, if I really need to I think I can set it to ~0.0001. The R and I stand for the Real and Imaginary parts respectively.

My question is how do I set this problem up for maple to solve, it has been giving me all sorts of problems which I don't know how to deal with.  I'm pretty sure there should be an exponential solution for small times.

If someone could provide the syntax for how to solve this using maple that would be great.

Thanks for the help.

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