Hello people in the mapleprimes,

I have a question, so I hope someone give me answers to it.

I calculated for the solution of the follwing differential equation.

restart

b:=diff(y(x),x)+a*y(x)=f(x);#where a and f(x) is not specified.

dsolve(b,y(x));

subs({f(x)=exp(x),a=2},%);where f(x) and a are specified.

c:=value(%);

The solution of the above was

y(x) = (1/3)*exp(x)+_C1/(exp(x))^2, (A)

where please note that the second term takes

the form of fraction _C/(exp(x))^2.

On the other hand, next I calculated the following differential equation where f(x) and a are specified from the start.

restart

d:=diff(y(x),x)+2*y(x)=exp(x);

dsolve(b,y(x));

Then,

y(x) = (1/3)*exp(x)+exp(-2*x)*_C1 (B)

was the obtained solution.

Each (A) and (B) are the same substantially mathematically. But, for Maple, the variable powered to minus brabra

is not the same as one over variable powered to brabra, so that (A) and (B) takes different forms, and maple will see them

different with each other.

Surely, with algsubs, algsubs(_C1/(exp(x))^2=exp(-2*x)*_C1,c) transforms (A) to (B).

But, I want to know whether there are some other ways than that to modify (A) to (B).

If there are any good ways for it, I will be happy if you teach them to me.

Thanks in advance.

taro