Write the the differential equation by separating the variables.
A)
B)
C)
D) No, the variables cannot be separated
E)

Question

​Write the the differential equation by separating the variables. ​  ​
A) ​ 
B) ​ 
C) ​ 
D) ​No, the variables cannot be separated 
E) ​

Quizplus · Accepted Answer

To separate variables, we need to express the equation as y' = f(x)g(y). Rearranging the given equation, we get:

(dy/dx) = sin(x)cos(y)

Now dividing both sides by cos(y), we get:

(1/cos(y))dy = sin(x)dx

Integrating both sides, we get:

ln(|sec(y)|) = -cos(x) + C

Taking exponential on both sides, we get:

|sec(y)| = e^(-cos(x) + C)

Now taking cases for the sign of sec(y), we get:

sec(y) = e^(-cos(x) + C)   or   sec(y) = -e^(-cos(x) + C)

Thus, the variables have been separated and the answer is option B.

​Write the The Differential Equation by Separating the Variables