Question: How can I scale a differential equation in Maple?

I am teaching a course in biofluid mechanics and am looking to help the students get more use out of Maple. Often it is advantageous to scale a differential equation (and initial conditions) using dimensionless variables to reduce the number of free parameters in a problem. For example, the simple linear oscillator differential equation:

Eq(1)         m*d2x(t)/dt2 + k*x(t)=0

where k and m are parameters.  If we define a dimensionless time, s=t/T, and a dimensionless position, X=x/L, where T and L are constants, , Eq(1) becomes

Eq(2)         (mL/T2 ) *d2X(s)/ds2 +  kL*X(s)=0

Then choosing T=sqrt(m/k) we arrive at

Eq(3)         d2X(s)/ds2 +  X(s)=0

which has no parameters.  Can this sequence be done in Maple for a differential equation...i.e. change of variables?


Please Wait...