Details

This message is generated when the given boundary conditions are not sufficient to fix all the arbitrary constants in the general solution.
Off[message] switches off the message; On[message] switches it on. For example: Off[DSolve::bvsing].

Examples

The initial conditions are specified at x == 0, which is a singular point for the ODE:

Wolfram Language code: eq = Derivative[2][y][x] - ((1 + x) Derivative[1][y][x]/x) + (y[x]/x) == 0 && y[0] == 1 && Derivative[1][y][0] == 1;

As a result, the solution depends on the arbitrary constant C[2]:

Wolfram Language code: sol = DSolve[eq, y, x]

Wolfram Language code: eq /. sol // Simplify

Avoid this problem by specifying the boundary conditions at a nearby nonsingular point:

Wolfram Language code:

eq1 = Derivative[2][y][x] - ((1 + x) Derivative[1][y][x]/x) + (y[x]/x) == 0 && y[(1/1000)] == 1 && Derivative[1][y][(1/1000)] == 1;

Wolfram Language code: sol = DSolve[eq1, y, x]

Wolfram Language code: eq1 /. sol // Simplify

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