Q115 / 170 · Manipal (MET) 2016 · Mathematics

The degree of the differential equation $x=1+\left(\frac{d y}{d x}\right)+\frac{1}{2!}\left(\frac{d y}{d x}\right)^2+\frac{1}{3!}\left(\frac{d y}{d x}\right)^3+\ldots$

  • A
    $3$
  • B
    $2$
  • Correct answer
    C
    $1$
  • D
    Not defined

Solution

Given, $x=1+\frac{d y}{d x}+\frac{1}{2!}\left(\frac{d y}{d x}\right)^2+\frac{1}{3!}\left(\frac{d y}{d x}\right)^3+\ldots$ or $x=e^{\frac{d y}{d x}}$ $\Rightarrow \quad \frac{d y}{d x}=\log _e x$ Hence, the degree of the above differential equation is 1.

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

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