AP EAMCET · Maths · Differential Equations
The solution of the differential equation \(\cos (x+y) d y=d x\) given that \(y(0)=0\) is
- A \(y=\tan \left(\frac{x+y}{2}\right)\)
- B \(y=\sin \left(\frac{x+y}{2}\right)\)
- C \(y=\tan \left(\frac{y}{2}\right)\)
- D \(y=\tan \left(\frac{x}{2}\right)\)
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 \(x+y=t \Rightarrow 1+\frac{d y}{d x}=\frac{d t}{d x}\)…
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