# Question:How to integrate exponential integrals in Maple? (Mathematica does the job)

## Question:How to integrate exponential integrals in Maple? (Mathematica does the job)

Hello,

I've been trying to force maple to find a solution of this differential equation:

ode := -((D@@2)(y))(r)-2*y(r)/r+y(r) = (2-V(r))*u[0](r)

dsolve(ode, y(r));

gives

`y(r) = r exp(-r) _C2 + (exp(r) + 2 exp(-r) Ei(1, -2 r) r) _C1 - 4             /  /  /             |1 | |    exp(-3 r) |- | |              |2 | |              \  \/                                  /   2    \             \           (exp(2 r) + 2 Ei(1, -2 r) r) \2 r  - 1/ exp(-2 r)   |           ------------------------------------------------- dr| exp(2 r)                          r                           |                                                               /                                                  \       /                1         \        |     + |Ei(1, -2 r) r + - exp(2 r)| (1 + r)| r     \                2         /        |                                           /  `
`(sorry, don't know yet how to copy 2-d math into chromium)`

As I mentioned in the caption, Mathematica does the job with ease:

eqn = -u''[r] - 2 u[r]/r + u[r] == (4/9 - Exp[-r]/r) 2 r Exp[-r]

and

DSolve[eqn, u[r], r][[1, 1, 2]] // FullSimplify

gives:

`1/9 E^(-2 r) (2 - 9 E^(3 r) C[2] +  E^r (-2 + r (-4 + 4 r + 9 C[1]) - 4 r ExpIntegralEi[-r] +   18 r C[2] ExpIntegralEi[2 r] + 4 r Log[2 r]))`

Where is the problem, how can I get the same solution using Maple?

Thank you!

Martin

﻿