Question:
The degree of the differential equation \(\frac{d^2y}{dx^2} + 3 \left( \frac{dy}{dx} \right)^2 = x^2 \log \left( \frac{d^2y}{dx^2} \right)\) is
The degree of the differential equation \(\frac{d^2y}{dx^2} + 3 \left( \frac{dy}{dx} \right)^2 = x^2 \log \left( \frac{d^2y}{dx^2} \right)\) is
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If any derivative appears inside functions like \(\log\), \(\sin\), \(e^x\), etc., then the degree is usually not defined.
Updated On: May 14, 2026
- \(1\)
- \(2\)
- \(3\)
- Not defined
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The Correct Option is D
Solution and Explanation
Concept:
The degree of a differential equation is defined only when the equation is a polynomial in its derivatives after removing radicals and fractions involving derivatives. ip
Step 1: Inspect the given differential equation.
The equation is: \[ \frac{d^2y}{dx^2}+3\left(\frac{dy}{dx}\right)^2=x^2\log\left(\frac{d^2y}{dx^2}\right) \] ip
Step 2: Check whether it is polynomial in derivatives.
The highest derivative \[ \frac{d^2y}{dx^2} \] appears inside a logarithm. So the equation is not polynomial in derivatives. ip
Step 3: Conclude about the degree.
Since the equation is not polynomial in derivatives, its degree is not defined. ip Hence, the correct answer is:
\[ \boxed{(D)\ \text{Not defined}} \]
The degree of a differential equation is defined only when the equation is a polynomial in its derivatives after removing radicals and fractions involving derivatives. ip
Step 1: Inspect the given differential equation.
The equation is: \[ \frac{d^2y}{dx^2}+3\left(\frac{dy}{dx}\right)^2=x^2\log\left(\frac{d^2y}{dx^2}\right) \] ip
Step 2: Check whether it is polynomial in derivatives.
The highest derivative \[ \frac{d^2y}{dx^2} \] appears inside a logarithm. So the equation is not polynomial in derivatives. ip
Step 3: Conclude about the degree.
Since the equation is not polynomial in derivatives, its degree is not defined. ip Hence, the correct answer is:
\[ \boxed{(D)\ \text{Not defined}} \]
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