Find the sum of the order and degree of the differential equation\[y = x \left( \frac{dy}{dx} \right)^3 + \frac{d^2 y}{d x^2}\]

Find the Sum of the Order and Degree of the Differential Equation Y = X ( D Y D X ) 3 + D 2 Y D X 2 - Mathematics

Question

Find the sum of the order and degree of the differential equation
$y = x {(\frac{d y}{d x})}^{3} + \frac{d^{2} y}{d x^{2}}$

Solution

The order is 2 as the highest derivative is 2.
The degree is 1 as the highest derivative is of order 1.
Hence, the sum of the order and degree of the differential equation
$y = x {(\frac{d y}{d x})}^{3} + \frac{d^{2} y}{d x^{2}}$

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Order and Degree of a Differential Equation

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Chapter 22: Differential Equations - Very Short Answers [Page 139]

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RD Sharma Mathematics [English] Class 12

Chapter 22 Differential Equations
Very Short Answers | Q 29 | Page 139

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