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
Show Hint
If a differential equation contains radicals or fractional powers of derivatives, first remove them. Then determine the degree from the power of the highest order derivative in the resulting polynomial equation.
Updated On: Jul 9, 2026
- \[ \frac32,\;2 \]
- \[ 2,\;3 \]
- \[ 2,\;2 \]
- \[ 3,\;4 \] \bigskip
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The Correct Option is C
Solution and Explanation
Concept:
• Order = highest order derivative present in the differential equation.
• Degree = power of the highest order derivative after removing radicals and fractional powers involving derivatives.
Step 1: Find the order. Given \[ \left(1+\left(\frac{dy}{dx}\right)^2\right)^{3/2} = \frac{d^2y}{dx^2}. \] The highest derivative present is \[ \frac{d^2y}{dx^2}. \] Hence, \[ \boxed{\text{Order}=2}. \]
Step 2: Remove the fractional power. Square both sides: \[ \left(1+\left(\frac{dy}{dx}\right)^2\right)^3 = \left(\frac{d^2y}{dx^2}\right)^2. \] Now the equation is polynomial in derivatives.
Step 3: Find the degree. The highest order derivative is \[ \frac{d^2y}{dx^2}, \] and its power is \[ 2. \] Therefore, \[ \boxed{\text{Degree}=2}. \]
Step 4: Write the final answer. \[ \boxed{(2,\,2)} \]
• Order = highest order derivative present in the differential equation.
• Degree = power of the highest order derivative after removing radicals and fractional powers involving derivatives.
Step 1: Find the order. Given \[ \left(1+\left(\frac{dy}{dx}\right)^2\right)^{3/2} = \frac{d^2y}{dx^2}. \] The highest derivative present is \[ \frac{d^2y}{dx^2}. \] Hence, \[ \boxed{\text{Order}=2}. \]
Step 2: Remove the fractional power. Square both sides: \[ \left(1+\left(\frac{dy}{dx}\right)^2\right)^3 = \left(\frac{d^2y}{dx^2}\right)^2. \] Now the equation is polynomial in derivatives.
Step 3: Find the degree. The highest order derivative is \[ \frac{d^2y}{dx^2}, \] and its power is \[ 2. \] Therefore, \[ \boxed{\text{Degree}=2}. \]
Step 4: Write the final answer. \[ \boxed{(2,\,2)} \]
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