## 50 Reputation

11 years, 44 days

## Proper application of "applyrule"...

Hi everyone,

I have a question regarding the use of the applyrule function. I have an expression that contains a polynomial. The expression looks something like:

Y := (a0 + a_1*x + a_2*x^2 + ... a_n*x^n)*f(y) + b_0 + b_1*x + b_2*x^2 + ... b_n*x^n)*g(y):

I would like to express this as y(x) = P_1*f(y) + P_2*g(y).

So far I have tried applyrule([a0 + a_1*x + a_2*x^2 + ... a_n*x^n = P_1, b_0 + b_1*x + b_2*x^2 + ... b_n*x^n) = P_2],Y):

This doesn't seem to work. Any suggestions?

## applyrule,subs,algsubs...

Hi Everyone,

I have an expression that contains a second order derivative: EXPR:=ay''(x) + bz'(x) + cf'(x)+... The variable y  obeys an ordinary differential equation, y''(x) = f(y,x). I would like to replace the second order deriavtive in my expression with f(y,x). So far I have tried applyrule([y''(x)=f(y,x)],EXPR), subs(y''(x)=f(y,x),EXPR) and algsubs(y''(x)=f(y,x),EXPR) and nothing seems to work. Any helpful suggestions?

## Simpliying an equation with RHS = 0...

Hi everyone,

I have a question regarding the simplification of an equation. Suppose I have and equation in maple such as (4*y^2 + 8*y + 8*sin(y))/(y^2 +1)=0. Is there a sequence of commands in Maple to simpliy this equation to (1/2)y^2 + y + sin(y)=0?

I know mulitplying the entire original equation by (1/8)*(y^2+1) would achieve the objective, but the equations I am generating are much longer and more complicated. The example above was chosen just to illustrate the goal.

Best,

Justin

## recognizing the root of a polynomial...

Hi everyone,

I have a maple program that generates a polynomial g(y)=(80y^8 + 68y^6 + 12y^4 -4y^2 -1). This polynomial has two real roots (irrational roots), call them +/- y*. My code does a sequential calculation, and often sI am left with a higher order polynomial in y that has the form h(y)= p(y)*g(y), where p(y) is also a polynomial in y. This polynomial h(y)=p(y)*g(y) is not in factored form (i.e. it would look like expand(p(y)*g(y)). Is there a way to instruct maple to recoginize that +/-y* is also a root h(y)=p(y)*g(y)? So far I've tried things like applyrule([g(y*)=0],h(y*)), but nothing seems to work (I suspect because Maple cannot recgonize that g(y) is a factor of h(y)). I am not interested in computing this numerically. I am just trying to find a way to instruct Maple to recognize symbolically that h(y*) =0.

Thanks a million for anyone who has any idea.

Best,

Justin

## defining the periodicity of an unknown f...

Hi,

Suppose you have an unknown function y(x)  that is 2*Pi periodic, i.e. (y(0) = y(2*Pi)). Is there a way to declare this in Maple? The reason I want to do this, is that if I integrate the derivative y'(x) of  this unknown function on [0,2*Pi]I would like Maple maple to be able to recognize that:

int(y'(x),x=0..2*Pi) =0

Thanks

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