Q92 / 150 · MHT CET 2026 (11 April Shift 1) · Mathematics
The order and degree of the differential equation $\sqrt{2 + \left(\dfrac{d^2 y}{dx^2}\right)^3} = \left(\dfrac{d^3 y}{dx^3}\right)^{5/2}$ respectively are
- A$2, 3$
- Correct answerB$3, 5$
- C$3, 2$
- D$5, 3$
Solution
The given differential equation is $\sqrt{2 + \left(\dfrac{d^2 y}{dx^2}\right)^3} = \left(\dfrac{d^3 y}{dx^3}\right)^{5/2}$
Squaring both sides to remove fractional powers, we get:
$2 + \left(\dfrac{d^2 y}{dx^2}\right)^3 = \left(\dfrac{d^3 y}{dx^3}\right)^5$
The highest order derivative present in the equation is $\dfrac{d^3 y}{dx^3}$, so the order of the differential equation is $3$.
The power of the highest order derivative is $5$, so the degree of the differential equation is $5$.
Therefore, the order and degree are $3$ and $5$ respectively.
Answer: $3, 5$
Squaring both sides to remove fractional powers, we get:
$2 + \left(\dfrac{d^2 y}{dx^2}\right)^3 = \left(\dfrac{d^3 y}{dx^3}\right)^5$
The highest order derivative present in the equation is $\dfrac{d^3 y}{dx^3}$, so the order of the differential equation is $3$.
The power of the highest order derivative is $5$, so the degree of the differential equation is $5$.
Therefore, the order and degree are $3$ and $5$ respectively.
Answer: $3, 5$
Hence, the correct answer is option: 'B'.