Q89 / 160 · TS EAMCET 2015 · Mathematics

The differential equation of the family of curves $y=a x+\frac{1}{a}$, where $a(\neq 0)$ is an arbitrary constant, has the degree

  • A
    4
  • B
    3
  • C
    1
  • Correct answer
    D
    2

Solution

We have, $$ \begin{aligned} y & =a x+\frac{1}{a} \\ \Rightarrow \quad \frac{d y}{d x} & =a \end{aligned} $$ On putting $a=\frac{d y}{d x}$ in Eq. (i), we get $$ \begin{array}{r} y=x \frac{d y}{d x}+\frac{1}{\left(\frac{d y}{d x}\right)} \\ \Rightarrow \quad y \frac{d y}{d x}=x\left(\frac{d y}{d x}\right)^2+1 \end{array} $$ which is a differential equation of degree 2 .

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

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