What is the general solution to the differential equation dy/dx = cos (8x) / cos (4y) ?

A. sin = (4y) - sin (8x) = C

B. sin (4y) - 2 sin (8x) = C

C. 2 sin (4y) - sin (8x) = C

D. 2 tan (4y) - sin (8x) = C

2sin4y - sin8x = K (C)

Step-by-step explanation:

Given the differential equation

dy/dx = cos (8x) / cos (4y)

This can be solved by using the variable separable method.

Step 1;

Separate the variables

Cos4ydy = cos 8xdx

step 2:

Integrate both sides of the equation

∫cos4y dy = ∫cos8x dx

sin4y/4 = sin8x/8

Step 3:

Add constant of integration to the side containing x variable

sin4y/4 = sin8x/8 + C

Taking sin8x to the other side we have:

sin4y/4-sin8x/8 = C

Multiplying through by 8:

2sin4y - sin8x = 8C

2sin4y - sin8x = K (where K = 8C)