mgu

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9 years, 46 days

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These are replies submitted by mgu

Hi again, Markiyan. It certainly worked. Thank you for the solution and the post as well.

Hi again, Markiyan. It certainly worked. Thank you for the solution and the post as well.

@Markiyan Hirnyk Hi Markiyan, I was hoping to avoid 'assuming' as it would speed up my calculation. This is not a stand-alone ODE; it is nested in a loop of calculation. Since we are using 'assuming', why n>4?

@Markiyan Hirnyk Hi Markiyan, I was hoping to avoid 'assuming' as it would speed up my calculation. This is not a stand-alone ODE; it is nested in a loop of calculation. Since we are using 'assuming', why n>4?

Hi Markiyan,

Your method worked for the ODE, but when I added the boundary conditions, Maple had trouble again. Specifically, with sol:=dsolve({Eq,R(1)=0,eval(diff(R(r),r),r=1)=0},R(r)), value(sol) did not resolve the integrals. Any suggestions? I am also wondering if there is a way to tell Maple to implement 'value' to begin with? Thanks for your help.

Hi Markiyan,

Your method worked for the ODE, but when I added the boundary conditions, Maple had trouble again. Specifically, with sol:=dsolve({Eq,R(1)=0,eval(diff(R(r),r),r=1)=0},R(r)), value(sol) did not resolve the integrals. Any suggestions? I am also wondering if there is a way to tell Maple to implement 'value' to begin with? Thanks for your help.

@pagan Hello again, pagan. The part that I did not get was why taking the limit after solving for C5 from the ode solution would yield the same result as solving for C5 from the coefficient in front of x^(-n+3). They seem to yield the same result, but the mathematics is not clear to me. Could you briefly explain it to me? Thank you.

@pagan Hello again, pagan. The part that I did not get was why taking the limit after solving for C5 from the ode solution would yield the same result as solving for C5 from the coefficient in front of x^(-n+3). They seem to yield the same result, but the mathematics is not clear to me. Could you briefly explain it to me? Thank you.

Hi pagan, I am trying to wrap my head around your use of limit in solving the remaining constant, say C5. Why is the limit of the isolated expression for C5 (i.e. solve(ans,indets(ans,name) minus indets(deqs,name))) as x approaches 0 from right equivalent to solving for the coefficient in front of x^(-n+3) that contains C5?

Hi pagan, I am trying to wrap my head around your use of limit in solving the remaining constant, say C5. Why is the limit of the isolated expression for C5 (i.e. solve(ans,indets(ans,name) minus indets(deqs,name))) as x approaches 0 from right equivalent to solving for the coefficient in front of x^(-n+3) that contains C5?

Hi pagan, I was hoping you would pick up the post here. Thanks, I will look into it.

Hi pagan, I was hoping you would pick up the post here. Thanks, I will look into it.

Hi,

Thank you for showing me that the identical results with the two different setups. However, the original problem remains unsolved. I would like to set up the ODE so that Maple can solve for all the constants automatically. This is crucial because I want to repeat the procedure for many other similar equations. I am quite certain it has something to do with the way I assumed the properties of n. If I leave the assumptions about n out, the solution will remain unchanged with one or two constants depending whether you include the D(y)(0) = D(y)(0) statement. That means the assumption made about n has not served any purpose in solving for the constants. What do you think of this?

Hi,

Thank you for showing me that the identical results with the two different setups. However, the original problem remains unsolved. I would like to set up the ODE so that Maple can solve for all the constants automatically. This is crucial because I want to repeat the procedure for many other similar equations. I am quite certain it has something to do with the way I assumed the properties of n. If I leave the assumptions about n out, the solution will remain unchanged with one or two constants depending whether you include the D(y)(0) = D(y)(0) statement. That means the assumption made about n has not served any purpose in solving for the constants. What do you think of this?

@pagan Hi pagan, thank you for your answer and patience. I tried your code and it worked for the specific case. By the way, when I changed the code to "assuming y(0)::finite", Maple aslo worked out the result. However, I have a follow-up question on the same subject. Please refer to the following lines of code.

restart;

dsolve({diff(y(x),x,x)+diff(y(x),x)/x-y(x)*(n^2)/(x^2)=-4*(n^2)/(x^2),y(1)=0,y(0)=y(0)})
    assuming y(0)::finite;

Maple returned "y(x)=x^n*C1+x^(-n)(-C1-4)+4". My intention was to ask Maple to solve the ODE assuming that n was a positive integer so that C1=-4 and the coefficient in front of x^(-n) would disappear. I tried to juxtapose another condition "n::posint" along with y(0)::finite in my assumption argument, but Maple complained that no assumption can be made about n as it is a constant.

Have you any suggestions? Thank you again for your help.

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