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:

54 km / hours

step-by-step explanation:

we need to convert seconds to hours

60 seconds = 1 minutes

60 minutes = 1hour

15 m         60 second   60 minutes

  * *         = 54000 meters/ hour

second     1 minute             1 hour

now we need to convert meters to km

1000 m = 1 km

54000 m       1 km

*   = 54 km / hours

hour               1000m