Write the Degree of the Differential Equation a 2 D 2 Y D X 2 = { 1 + ( D Y D X ) 2 } 1 / 4

Question

Write the degree of the differential equation
\[a^2 \frac{d^2 y}{d x^2} = \left\{ 1 + \left( \frac{dy}{dx} \right)^2 \right\}^{1/4}\]

Solution

We have,
\[ a^2 \frac{d^2 y}{d x^2} = \left\{ 1 + \left( \frac{dy}{dx} \right)^2 \right\}^{1/4} \]
\[ \left\{ a^2 \frac{d^2 y}{d x^2} \right\}^4 = 1 + \left( \frac{dy}{dx} \right)^2 \]
Degree of the differential equation is the degree of the highest order derivative .
Therefore, the degree must be 4 .

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Order and Degree of a Differential Equation

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Chapter 21: Differential Equations - Very Short Answers [Page 138]

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R.D. Sharma Mathematics Volume 1 and 2 [English] Class 12

Chapter 21 Differential Equations
Very Short Answers | Q 7 | Page 138

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