Q268 / 270 · NDA 2021 (Phase 2) · Mathematics
What is the differential equation of $y=A-\frac{B}{x}$ ?
- A$x y_2+y_1=0$
- Correct answerB$x y_2+2 y_1=0$
- C$x y_2-2 y_1=0$
- D$2 x y_2+y_1=0$
Solution
General solution, $y=A-\frac{B}{x}$
$\begin{aligned}
& y_1=-B\left(-\frac{1}{x^2}\right)=\frac{B}{x^2} \\
& x^2 y_1=B \\
& x^2 y_2+y_1 \times 2 x=0 \\
& \therefore \quad x\left(x y_2+2 y_1\right)=0
\end{aligned}$
Differential Equation : $x y_2+2 y_1=0$
Hence, the correct answer is option: 'B'.