# Question:why Maple dsolve with series requires IC to be same point as expansion point?

## Question:why Maple dsolve with series requires IC to be same point as expansion point?

Maple 2023

Is there a mathematical reason why Maple does not allow expansion point for solving an ode using series solution to be different than where initial conditions are located?

I do not see why this restriction is there. Here is first order ode, where expansion point is x=1 and initial condiitons are also at x=1

```restart;
ode:=diff(y(x),x)=x^3;
dsolve([ode,y(1)=1],y(x),'series',x=1)
```

y(x) = (1 + (x - 1)) + 3/2*(x - 1)^2 + (x - 1)^3 + 1/4*(x - 1)^4 + O((x - 1)^6)

No problem. But when expansion point at x=0, it complains

```restart;
ode:=diff(y(x),x)=x^3;
dsolve([ode,y(1)=1],y(x),'series',x=0)
```

Error, (in dsolve/SERIES) conflicting specifications of the series expansion point: 1 v.s. 0

I know help mentions that it uses initial conditions point for expansion if given, and if no IC is given, then it uses x=point if given and if no x=point is given then it default to x=0.

But my question is, why it does not handle the case when the expansion point is given explicitly and is at a different location than where IC are given? Is this simply just a feature missing that could be added in a future release if needed, or is it due to some mathematical reason that I do not see?

I would have expected it to first find the series solution around the given expansion point, then use the IC to determine the unknown constant after that, just like we normally do when solving an ode using standard methods not using series expansion.

I am using Maple 2023

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