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?