Question:
The degree of the differential equation \(\left(\frac{d^2y}{dx^2}\right)^2 + \left(\frac{dy}{dx}\right)^2 = x\sin\left(\frac{d^2y}{dx^2}\right)\) is
The degree of the differential equation \(\left(\frac{d^2y}{dx^2}\right)^2 + \left(\frac{dy}{dx}\right)^2 = x\sin\left(\frac{d^2y}{dx^2}\right)\) is
Show Hint
Degree is defined only when the differential equation is a polynomial in derivatives.
Updated On: Apr 23, 2026
- 1
- 2
- 3
- None of these
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Verified By Collegedunia
The Correct Option is D
Solution and Explanation
Step 1: Formula / Definition}
\[ \text{Degree defined only for polynomial in derivatives} \]
Step 2: Calculation / Simplification}
The equation contains \(\sin\left(\frac{d^2y}{dx^2}\right)\), which is not a polynomial in derivatives.
\(\therefore\) Degree is not defined.
Step 3: Final Answer
\[ \text{Not defined} \]
\[ \text{Degree defined only for polynomial in derivatives} \]
Step 2: Calculation / Simplification}
The equation contains \(\sin\left(\frac{d^2y}{dx^2}\right)\), which is not a polynomial in derivatives.
\(\therefore\) Degree is not defined.
Step 3: Final Answer
\[ \text{Not defined} \]
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