Q118 / 160 · AP EAMCET 2022 (07 Jul Shift 2) · Mathematics

If $a$ and $b$ are respectively the order and degree of a differential equation $y^2\left(y^{\prime \prime}\right)^2+3 x\left(y^{\prime}\right)^{1 / 3}+x^2 y^2=\sin x$, then

  • A
    $b=a$
  • B
    $a=3 b$
  • Correct answer
    C
    $b=3 a$
  • D
    $a b=6$

Solution

$\begin{aligned} & (c) y^2 \cdot\left(y^{\prime \prime}\right)^2+3 x(y)^{1 / 3}+x^2 y^2=\sin x \\ & \Rightarrow\left(y^2 \cdot\left(y^{\prime \prime}\right)^2+x^2 \cdot y^2-\sin x\right)^3=27 x^3\left(y^{\prime}\right) \\ & \therefore \text { Order }=a=2, \text { Degree }=b=6 \\ & \therefore \quad b=3 a\end{aligned}$

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

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