Show that an implicit solution of 2x sin2(y) dx - (x2 + 11) cos(y) dy = 0 is given by ln(x2 + 11) + csc(y) = C. Differentiating ln(x2 + 11) + csc(y) = C we get 2x/ x2 + 11 (__) dy/dy=0 or
2x sin2(y) dx + ()dy = 0.
Find the constant solutions, if any, that were lost in the solution of the differential equation. (Let k represent an arbitrary integer.)
y =

From the question we are told that

  The  equation is  

Generally the goal of this solution is to prove that the implicit solution of the differential  equation above is  

First Step  

    Differentiate the solution with respect to  x  

=>  

=>  

=>  

multiply through by   , ,

So

=>

Looking at the equation obtained we see that it is equivalent to the differential  equation hence  the implicit solution of is  

Step-by-step explanation: