# DSolve expression doesn't evaluate

Can Mathematica solve $\; d^2/dx^2{}+ (1/x) d/dx\;$ form of equations?
For example, I am trying to solve the system of equations given below:

eqn1 = D[w[x], {x, 2}] + (1/x) (D[w[x], x]) - w[x];
eqn2 = D[v[x], {x, 2}] + (1/x) (D[v[x], x]) - (v[x] - u[x]);
eqn3 = D[u[x], {x, 2}] + (1/x) (D[u[x], x]) + v[x] - u[x] - w[x];
eqnSet = {eqn1 == 0, eqn2 == 0, eqn3 == 0, w[1] == 0, v[1] == 0,
u[1] == 0, w'[0] == 0, v'[0] == 0, u'[0] == 0};
DSolve[eqnSet, {w[x], v[x], u[x]}, x]


I am getting DSolve returning the input statement unevaluated.

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Is this 1/x term OK if you specify conditions for x=0? –  Sjoerd C. de Vries Jun 25 '13 at 21:56
This DSolve[{x D[w[x], {x, 2}] + (D[w[x], x]) - x w[x] == 0, w[1] == 0, w'[0] == 0}, w[x], x] works but due to the initial conditions it's a trivial solution. –  b.gatessucks Jun 25 '13 at 21:57
I missed to see that. Thanks to both of you for pointing out my negligence. Still do we need NDSolve[] or can DSolve[] do the job? –  user8250 Jun 25 '13 at 23:13
Just try and see. –  b.gatessucks Jun 26 '13 at 5:01