Hello all, I'm new to solving system of differential equations
numerically. I am trying to integrate with respect to time 2 transport equations which are coupled. It is initial value problem and solution
of j-1 equation is a parameter in the next equation. I tried using
forward Euler as a first attempt to compute the solution but after some iterations the values of the variables are apporaching either
zero/infinity.

Here are the system of equations (changed variable name for simplicity)

dy/dt = constant - (constant * (y)^(1/6) * z^(1/6))
dz/dt = k1*constant + (k2*temperature* (y)^(1/2)*(z/y)^(1/3)) - ((k3*temperature* (y)*(6*z*rho/(pi*y))^(2/3)) - ((k*4temperature* (y)*(z/y)^(1/3))

In the above equation I know initial values of y & z. Also the
constants in expression are numerical values being calculated from an
input data file in every iteration.

I would like to know how to integrate the above expression which looks complicated with so many exponents and coupling. Kindly guide me to a
proper solution or to any literature where I can find solution to these
type of engineering problems.

Regards

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