Find a second solution y2(x) of
x^2y"-3xy'+5y=0; y1=x^2cos(lnx)

We can try reduction order and look for a solution . Then

Substituting these into the ODE gives

which leaves us with an ODE linear in :

This ODE is separable; divide both sides by the coefficient of and separate the variables to get

Integrate both sides; on the right, substitute so that .

Now solve for ,

then for ,

Solve for by integrating both sides.

Substitute again and solve for :

then for ,

So the second solution would be

already accounts for the second term of the solution above, so we end up with

as the second independent solution.

hi there!

the answer will be d: 2

27 + 13x + 15 = (x + 5)( =

step-by-step explanation:

27 + 13x + 15 = (x + 5)( = 27 + 13x + 15 = (x + 5)( = 27 + 13x + 15 = (x + 5)( =