software_c

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These are answers submitted by software_c

eqn1:= (1/2)*p+1+(-4*p^2-p-1)/(3*p^3+7*p^2+2*p+2):
a := addressof(eqn1):
d := disassemble(a):
kernelopts(dagtag = d[1]):  ##Optional. Just as a check that it is a SUM.
eqn1a := pointto(d[2])*pointto(d[3]);

output: (1/2)*p

 

It seems you can do a double substitution for each unknown power of x. Then undo the substitution to get the answer you need. Exmple below.

eqn1 := a*x^b+x^b

                               a*x^b+x^b

subs(y = x^b, collect(subs(x^b = y, eqn1), [y], recursive))

                              (a+1)*x^b

 

Not sure if this is useful as you will have to make a substitution for every unknown power of x but hope that helps.

Use of dsolve and plot functions with Explore option should help you.

 

Below is an example of how to use dsolve. You should be able to talor to your particular equation. 

 

ode := diff(y(x), x, x) = 2*y(x)+1

ics := y(0) = 1, (D(y))(0) = 0

dsolve({ics, ode})

 

NOTE: ics does not need to be initial conditions. For example y(1)=0 is also valid.

 

Then copy the RHS for Y(x) and paste onto a new line. The rightclick and use plots to plot. Defining an arbitrary variable in your original equations will allow you to use Explore command (also in rightclick popup menu) to explore the modulation.

 

Hope that helps.

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