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X 2 ( D 2 Y D X 2 ) 3 + Y ( D Y D X ) 4 + Y 4 = 0 - Mathematics

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Question

\[x^2 \left( \frac{d^2 y}{d x^2} \right)^3 + y \left( \frac{dy}{dx} \right)^4 + y^4 = 0\]

Solution

\[x^2 \left( \frac{d^2 y}{d x^2} \right)^3 + y \left( \frac{dy}{dx} \right)^4 + y^4 = 0\]
In this differential equation, the order of the highest order derivative is 2 and its power is 3. So, it is a differential equation of order 2 and degree 3.
It is a non-linear differential equation, as its degree is more than 1.
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Chapter 22: Differential Equations - Exercise 22.01 [Page 5]

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RD Sharma Mathematics [English] Class 12
Chapter 22 Differential Equations
Exercise 22.01 | Q 11 | Page 5

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