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Contact [7]
3 years ago
14

Please help I don't understand this ?

Mathematics
1 answer:
elixir [45]3 years ago
6 0
The answer is C. I guess...
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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.
Dvinal [7]

Answer:

From the question we are told that

  The  equation is  2x sin^2(y) dx - (x^2 + 11) cos(y) dy = 0

Generally the goal of this solution is to prove that the implicit solution of the differential  equation above is  ln(x^2 + 11) + csc(y) = C.

First Step  

    Differentiate the solution with respect to  x  

   0  = \frac{2x}{ x^2 + 11}  + [-cot * csc(y) ]\frac{dy}{dx}

=> 0 =  \frac{2x}{ x^2 + 11}  + [-\frac{cos(y)}{ sin(y) }* \frac{1}{sin(y)}  ]\frac{dy}{dx}  

=>  0  =  \frac{2x}{ x^2 + 11}  + [-\frac{cos(y)}{ sin^2(y) }]\frac{dy}{dx}

=>  

multiply through by  sin^2(y) , x^2 + 11, dx

So

=> 2 x (sin^2(y) dx  + [-cos(y) (x^2 + 11)]dy = 0

Looking at the equation obtained we see that it is equivalent to the differential  equation hence  the implicit solution of 2x sin^2(y) dx - (x^2 + 11) cos(y) dy = 0 is   ln(x^2 + 11) + csc(y) = C.

Step-by-step explanation:

     

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