AP EAMCET · Maths · Differential Equations
The general solution of the differential equation \(\cos (x+y) d y=d x\) is
- A \(y=\tan \left(\frac{x+y}{2}\right)+c\)
- B \(y=\sec \left(\frac{x+y}{2}\right)+c\)
- C \(y=x \sec \left(\frac{y}{x}\right)+c\)
- D \(y=-\cos ^{-1}\left(\frac{y}{x}\right)+c\)
Answer & Solution
Correct Answer
(A) \(y=\tan \left(\frac{x+y}{2}\right)+c\)
Step-by-step Solution
Detailed explanation
\(\frac{dy}{dx} = \frac{1}{\cos(x+y)}\) Let \(u = x+y \implies \frac{du}{dx} = 1 + \frac{dy}{dx}\) \(\frac{du}{dx} - 1 = \frac{1}{\cos(u)}\) \(\frac{du}{dx} = 1 + \frac{1}{\cos(u)} = \frac{\cos(u)+1}{\cos(u)}\) \(\int \frac{\cos(u)}{\cos(u)+1} du = \int dx\)…
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