Question

solve the differential equation that satisfies the given condition:

dy/dx=(ycos(x))/(6+y^2), y(0)=1

Answer 1

y' = (y cosx)/(6+y^2)

(6+y^2)/y dy = cosx dx

6lny + 1/2 y^2 = sinx + c
y^2 + 12lny = 2sinx + c

I don't see any way to express y explicitly as a function of x, using elementary functions.