TS EAMCET · Maths · Differential Equations
The general solution of the differential equation \(x \cos \frac{y}{x}(y d x+x d y)=y \sin \frac{y}{x}(x d y-y d x)\) is
- A \(\log (x y)=\log \cos \frac{x}{y}+C\)
- B \(\cos \left(\frac{y}{x}\right)=\frac{C}{x y}\)
- C \(\log (x y)=\log \sec \frac{x}{y}+C\)
- D \(x+y+C=0\)
Answer & Solution
Correct Answer
(B) \(\cos \left(\frac{y}{x}\right)=\frac{C}{x y}\)
Step-by-step Solution
Detailed explanation
We have, \(x \cos \left(\frac{y}{x}\right)(y d x+x d y)\) \(=y \sin \frac{y}{x}(x d y-y d x)\) \(\Rightarrow \quad x y \sin \left(\frac{y}{x}\right) d y-y^2 \sin \left(\frac{y}{x}\right) d x\) \(=x y \cos \left(\frac{y}{x}\right) d x+x^2 \cos \left(\frac{y}{x}\right) d y\)…
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