Q120 / 160 · AP EAMCET 2024 (21 May Shift 2) · Mathematics

$\frac{d y}{d x}=\frac{y+x \tan \frac{y}{x}}{x} \Rightarrow \sin \frac{y}{x}=$

  • A
    $c x^2$
  • Correct answer
    B
    $c x$
  • C
    $c x^3$
  • D
    $c x^4$

Solution

$\begin{aligned} & \text { Let } y=v x \Rightarrow \frac{d y^2}{d x}=v+x \frac{d v}{d x} \\ & \begin{aligned} \Rightarrow v+x \frac{d v}{d x} & =v+\tan v \Rightarrow \int \frac{\cos v}{\sin v} d v=\int \frac{d x}{x} \\ & =\ln (\sin v)=\ell \operatorname{n} x+C^{\prime}\end{aligned} \\ & \sin v=C x \Rightarrow \sin \left(\frac{y}{x}\right)=C x\end{aligned}$

Hence, the correct answer is option: 'B'.

Relevant Questions