TS EAMCET · Maths · Differential Equations
The general solution of the differential equation \(\left(x \sin \frac{y}{x}\right) d y=\left(y \sin \frac{y}{x}-x\right) d x\) is
- A \(\sin ^{-1}\left(\frac{y}{x}\right)=\frac{x}{2}+c\)
- B \(\sin \left(\frac{x}{y}\right)=\frac{x^2}{2}+c\)
- C \(\sin \left(\frac{y}{x}\right)=\log |x|+c\)
- D \(\cos \left(\frac{y}{x}\right)=\log |x|+c\)
Answer & Solution
Correct Answer
(D) \(\cos \left(\frac{y}{x}\right)=\log |x|+c\)
Step-by-step Solution
Detailed explanation
\begin{aligned} & \text { (x) } \\ & \left(x \sin \frac{y}{x}\right) d y=\left(y \sin \frac{y}{x}-x\right) d x \\ & \Rightarrow \frac{d y}{d x}=\frac{y \sin \frac{y}{x}-x}{x \sin \frac{y}{x}} \Rightarrow \frac{d y}{d x}=\frac{y}{x}-\operatorname{cosec} \frac{y}{x} \\ & \text {…
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