Wolfram Mathematica 7 routinely confuses sums with integrals.This
Example 1:
DSolve[(-Log[Log[a]] f'[x] + f''[x])/(Log[a] f'[x]) == D[Sum[f[x], x], x], f[x], x]
g[x_] := f[x] /. s
g[x]
Checking the result by inserting it into the equation shows the result is just one exampleincorrect:
http://www.wolframalpha.com/input/?i=derivative+sum+2^(1/k)+from+0+to+x-1
$$\frac{\partial}{\partial x}\sum_0^{x-1} 2^{1/k}
(-Log[Log[a]] g'[x] + g''[x])/(Log[a] g'[x]) - D[Sum[g[x], x], x]
Example 2:
s=NDSolve[{0.9159460564995328*Derivative[1][f][x] =2^{1/k}$$= f[x]*Product[f[x], x], f[0] == 1}, f, {x, -1.9, 15}]
Plot[Evaluate[f[x] /. s], {x, -0.4, 1.5}, AspectRatio -> Automatic, AxesOrigin -> {0, 0}]
In Mathematica 8.0 this has been fixed (i.e. it will report inability to solve the equations.
