ODE coefficients

one way

Comment on 2008-11-22 15:58 from jakubi ( Maple Rating 4

943)

is with differential operators:

with(DEtools):
_Envdiffopdomain:=[Dx,x]:
ode:=p(x,a)* diff(w(x),x$2) + q(x,a)* diff(w(x),x) + r(x,a)* w(x);

                    / 2      \
                    |d       |           /d      \
     ode := p(x, a) |--- w(x)| + q(x, a) |-- w(x)| + r(x, a) w(x)
                    |  2     |           \dx     /
                    \dx      /

dop:=de2diffop(ode,w(x));

                               2
              dop := p(x, a) Dx  + q(x, a) Dx + r(x, a)

coeff(dop,Dx,2);

                               p(x, a)

coeff

Comment on 2008-11-23 02:52 from Robert Israel ( Maple Rating 4

1554)

> Q:=p(x,a) *diff(w(x),x$2) + q(x,a) *diff(w(x),x) + r(x,a)* w(x);
   coeff(Q,diff(w(x),x$2));

coeff of Differential operator

Comment on 2008-11-27 17:14 from Sandor Szabo ( Maple Rating 2

119)

Hi Robert,

Something is wrong with your solution, coeff(Q,diff(w(x),x$2)) works well, but

coeff(Q,diff(w(x),x$1)) or coeff(Q,diff(w(x),x)) not. I absolutely don't understand why.

jakubi

Luckily, jakubi's solution works well. In fact I don't understand every detail, but very strange for me, that in Help there is coeff - extract a coefficient of a polynomial.

I suspect that in jacubi's solution dop is somehow a polynomial differential operator that is the reason that Maple can apply coeff.

Thanks, Sandor

oops

Comment on 2008-11-28 02:07 from Robert Israel ( Maple Rating 4

1554)

Sorry, I should have realized that this might not work, because diff(w(x),x) "occurs" inside diff(w(x),x$2) , which is actually stored as diff(diff(w(x),x),x).

coefficient of a polynomial

Comment on 2008-11-28 15:02 from jakubi ( Maple Rating 4

943)

For sure, 'coeff' should work for polynomials. Hence, the idea is to get the differential operator for this ODE, that 'de2diffop' writes as a polynomial in 'Dx', which represents d/dx.

Another way

Comment on 2008-11-28 15:21 from alec ( Maple Rating 4

1604)

Depending on the situation, the following also might work,

ode:=p(x,a)* diff(w(x),x$2) + q(x,a)* diff(w(x),x$2) + r(x,a)* w(x);

                    / 2      \
                    |d       |           /d      \
     ode := p(x, a) |--- w(x)| + q(x, a) |-- w(x)| + r(x, a) w(x)
                    |  2     |           \dx     /
                    \dx      /

subs(diff(w(x),x$2)=1, diff(w(x),x)=0, w(x)=0, ode);

                               p(x, a)

subs(diff(w(x),x$2)=0, diff(w(x),x)=1, w(x)=0, ode);

                               q(x, a)

subs(diff(w(x),x$2)=0, diff(w(x),x)=0, w(x)=1, ode);

                               r(x, a)

Alec