Question:
The differential equation which represents the family \( y^2 = 2c(x+\sqrt{c}) \) is
The differential equation which represents the family \( y^2 = 2c(x+\sqrt{c}) \) is
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Order depends only on highest derivative.
Updated On: Apr 30, 2026
- order 2
- degree 2
- order 3
- degree 3
- degree 1
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The Correct Option is A
Solution and Explanation
Concept:
Order = highest derivative present.
Step 1: Differentiate equation. \[ y^2 = 2c(x+\sqrt{c}) \] Differentiate: \[ 2y \frac{dy}{dx} = 2c \]
Step 2: Eliminate constant. Differentiate again: \[ 2\left(\frac{dy}{dx}\right)^2 + 2y \frac{d^2y}{dx^2} = 0 \]
Step 3: Conclusion. Highest derivative is second derivative ⇒ order = 2
Step 1: Differentiate equation. \[ y^2 = 2c(x+\sqrt{c}) \] Differentiate: \[ 2y \frac{dy}{dx} = 2c \]
Step 2: Eliminate constant. Differentiate again: \[ 2\left(\frac{dy}{dx}\right)^2 + 2y \frac{d^2y}{dx^2} = 0 \]
Step 3: Conclusion. Highest derivative is second derivative ⇒ order = 2
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