Question:
Solve $\cos(x+y)dy=dx$
Solve $\cos(x+y)dy=dx$
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Use substitution $u=x+y$ for combined-angle differential equations.
Updated On: Jun 10, 2026
- $y=\tan\frac{x+y}{2}+c$
- $y=x\sec(y/x)+c$
- $y=-\cos^{-1}(y/x)+c$
- $y=\tan(x+y)+c$
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The Correct Option is A
Solution and Explanation
Let \(u=x+y\)
\[
\frac{du}{dx}=1+\frac{dy}{dx}
\]
\[
\frac{dy}{dx}=\sec u
\]
\[
\frac{du}{dx}=1+\sec u
\]
\[
\frac{du}{1+\sec u}=dx
\]
Integrating:
\[
y=\tan\frac{x+y}{2}+c
\]
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