# Question:problems with odetest applied to series solution where indicial equation has complex roots

## Question:problems with odetest applied to series solution where indicial equation has complex roots

Maple 2022

To Maple support:

I see 2 problems here. Maple solves the ode using series method.

First problem: Using odetest shows the syntax according to help does not work. Which is

odetest(sol, ODE, series, point = 0);

The above gives internal error.

When changing to the following syntax

odetest(sol,ODE,type='series',point=0);

No internal error.

So help page should be corrected.

The second problem is that Maple odetest does not return 0 on its own solution. I verified manually that the solution is correct actually. So I do not know why maple does not return zero here. Simplfication does not help.

 > interface(version);

 > restart;
 > Order:=6; ode:=x^2*diff(diff(y(x),x),x)+x^2*diff(y(x),x)+y(x) = 0; maple_sol:=dsolve(ode,y(x),type='series',x=0): odetest(maple_sol,ode,series,point=0); odetest(maple_sol,ode,'series',point=0);

Error, (in odetest/series) complex argument to max/min: 13/2-1/2*I*3^(1/2)

Error, (in odetest/series) complex argument to max/min: 13/2-1/2*I*3^(1/2)

 > odetest(maple_sol,ode,type='series',point=0); #This should return zero, but it does not.

 >