Maths · The solution of differential equation by the method of separation of variables
Solution of the differential equation is
Solution of the differential equation \( \tan y \cdot \sec ^{2} x d x+\tan x \cdot \sec ^{2} y d y=0 \) is
- A. \( \tan x+\tan y=k \)
- B. \( \tan x-\tan y=k \)
- C. \( \frac{\tan x}{\tan y}=k \)
- D. \( \tan x \cdot \tan y=k \)
Step-by-step solution
The given differential equation is exact. On separating variables, we get (sec^2 x / tan x) dx = - (sec^2 y / tan y) dy. Integrating both sides gives ln|tan x| = -ln|tan y| + C, which simplifies to ln|tan x tan y| = C, implying tan x tan y = constant = k.
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