TS EAMCET · Maths · Differential Equations
The general solution of the differential equation \(\cos (x+y) d y=d x\) is
- A \(y=\sec (x+y)+c\)
- B \(y-\tan \frac{y}{2}=x+c\)
- C \(y=\tan \left(\frac{x+y}{2}\right)+c\)
- D \(y=\frac{1}{2} \tan (x+y)+c\)
Answer & Solution
Correct Answer
(C) \(y=\tan \left(\frac{x+y}{2}\right)+c\)
Step-by-step Solution
Detailed explanation
\(\frac{d x}{d y}=\cos (x+y)\) Let \(\quad x+y=v \quad \Rightarrow \frac{d x}{d y}+1=\frac{d v}{d y}\) So, \(\quad \frac{d x}{d y}=\frac{d v}{d y}-1 \Rightarrow \frac{d v}{d y}-1=\cos v\)…
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