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D 2 Y D X 2 + 3 ( D Y D X ) 2 = X 2 Log ( D 2 Y D X 2 )

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Question

\[\frac{d^2 y}{d x^2} + 3 \left( \frac{dy}{dx} \right)^2 = x^2 \log\left( \frac{d^2 y}{d x^2} \right)\]
One Line Answer
Sum
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Solution

\[\frac{d^2 y}{d x^2} + 3 \left( \frac{dy}{dx} \right)^2 = x^2 \log \left( \frac{d^2 y}{d x^2} \right)\]
In this differential equation, the order of the highest order derivative is 2.
Clearly, the R.H.S. of the differential equation cannot be expressed as a polynomial in \[\frac{d^2 y}{d x^2}\]
Thus, its degree is not defined.
The order of the differential equation is 2 and its degree is not defined.
It is a non-linear differential equation, as one of its differential co-efficients, that is, \[\left( \frac{dy}{dx} \right)\], has exponent 2, which is greater than 1.

 

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Chapter 21: Differential Equations - Exercise 22.01 [Page 5]

APPEARS IN

R.D. Sharma Mathematics Volume 1 and 2 [English] Class 12
Chapter 21 Differential Equations
Exercise 22.01 | Q 20 | Page 5

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