Question:
The order and degree of the differential equation $\left[1 + \left(\frac{dy}{dx}\right)^2\right]^{3/2} = \frac{d^2y}{dx^2}$ are respectively:
The order and degree of the differential equation $\left[1 + \left(\frac{dy}{dx}\right)^2\right]^{3/2} = \frac{d^2y}{dx^2}$ are respectively:
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Always clear fractional indices first! The degree of a differential equation can only be defined when it is written as a polynomial in its derivatives.
Updated On: May 31, 2026
- $2$ and $2$
- $2$ and $3$
- $1$ and $2$
- $2$ and $1$
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The Correct Option is A
Solution and Explanation
Step 1: Concept
The order of a differential equation is the order of the highest derivative present. The degree is the power of this highest derivative after the equation is cleared of fractional powers and radicals.
Step 2: Meaning
We need to eliminate the fractional exponent $\frac{3}{2}$ on the left-hand side before analyzing the degree of the equation.
Step 3: Analysis
The given equation is: \[ \left[1 + \left(\frac{dy}{dx}\right)^2\right]^{3/2} = \frac{d^2y}{dx^2} \] To remove the fraction $\frac{3}{2}$, we square both sides: \[ \left[1 + \left(\frac{dy}{dx}\right)^2\right]^3 = \left(\frac{d^2y}{dx^2}\right)^2 \] Now analyze the equation:
• The highest derivative present is $\frac{d^2y}{dx^2}$, which is of second order. Thus, Order = $2$.
• The power of this highest derivative is $2$. Thus, Degree = $2$.
Step 4: Conclusion
The order and degree of the differential equation are $2$ and $2$ respectively. Final Answer: (A)
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