Question:
(b) Solve the differential equation \( \sec^2 x \tan y \, dx + \sec^2 y \tan x \, dy = 0 \).
(b) Solve the differential equation \( \sec^2 x \tan y \, dx + \sec^2 y \tan x \, dy = 0 \).
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Separate variables for trigonometric differential equations before integration.
Updated On: Mar 1, 2025
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Solution and Explanation
Rewritetheequation:
\[
\frac{\tany}{\sec^2y}\,dy=-\frac{\tanx}{\sec^2x}\,dx.
\]
Integratingbothsides:
\[
\int\siny\,dy=-\int\sinx\,dx.
\]
\[
-\cosy=\cosx+C.
\]
Simplify:
\[
\cosx+\cosy=C.
\]
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