Find the general solution of the given differential equation

Find the general solution of the given differential equation. x^2y\' + xy = 2 y = 1/x middot C_1 + 2 In(x)/x Give the largest interval I over which the general solution is defined. (Think about the implications of any singular points.) (-infinity, infinity) (2, infinity) [0, infinity) (0, infinity) (0, 2) Determine whether there are any transient terms in the general solution. (Enter the transient terms as a comma-separated list; if there are none, enter NONE.) 1/x middot C_1, 2 In(x)/x

Solution

P(x)=1/x^2 and Q(x)=2/x^2 is discontinuous at x=0.

Hence interval is (0,infinity)