AP EAMCET · Maths · Differential Equations
The solution of the differential equation \(x \frac{d y}{d x}=y-x \tan \left(\frac{y}{x}\right)\) is (Here, \(k\) is an arbitrary constant)
- A \(x=y \sin ^{-1}\left(\frac{k}{x}\right)\)
- B \(y=x \sin ^{-1}\left(\frac{k}{x}\right)\)
- C \(x \sin y+k=0\)
- D \(y=x \cos (k x)\)
Answer & Solution
Correct Answer
(B) \(y=x \sin ^{-1}\left(\frac{k}{x}\right)\)
Step-by-step Solution
Detailed explanation
Given differential equation is \(\begin{aligned} \quad x \frac{d y}{d x} & =y-x \tan \frac{y}{x} \\ \Rightarrow \quad & \frac{d y}{d x}=\frac{y}{x}-\tan \left(\frac{y}{x}\right) \end{aligned}\) Let \(\quad y=v \cdot x\) \(\Rightarrow \quad \frac{d y}{d x}=v+x \frac{d v}{d x}\)…
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