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AP EAMCET · Maths · Differential Equations

The solution of the differential equation \(\cos (x+y) d y=d x\) given that \(y(0)=0\) is

  1. A \(y=\tan \left(\frac{x+y}{2}\right)\)
  2. B \(y=\sin \left(\frac{x+y}{2}\right)\)
  3. C \(y=\tan \left(\frac{y}{2}\right)\)
  4. D \(y=\tan \left(\frac{x}{2}\right)\)
Verified Solution

Answer & Solution

Correct Answer

(A) \(y=\tan \left(\frac{x+y}{2}\right)\)

Step-by-step Solution

Detailed explanation

Given differential equation \(\cos (x+y) d y=d x \Rightarrow \frac{d y}{d x}=\sec (x+y)\) Put \(x+y=t \Rightarrow 1+\frac{d y}{d x}=\frac{d t}{d x}\)…