Question:
The degree of the differential equation \( (y'')^2 + (y')^3 = x \sin(y') \) is:
The degree of the differential equation \( (y'')^2 + (y')^3 = x \sin(y') \) is:
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The degree of a differential equation is undefined if any non-polynomial terms involve derivatives.
Updated On: Jan 27, 2025
- \( 1 \)
- \( 2 \)
- \( 3 \)
- Not defined
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The Correct Option is D
Solution and Explanation
Step 1: Definition of degree.
The degree of a differential equation is defined only when the equation is polynomial in all derivatives. Step 2: Analyze the equation.
The given equation: \[ (y'')^2 + (y')^3 = x \sin(y'), \] contains a non-polynomial term \( \sin(y') \). Hence, the degree is not defined. Step 3: Conclusion.
The degree is: \[ \boxed{\text{Not defined}}. \]
The degree of a differential equation is defined only when the equation is polynomial in all derivatives. Step 2: Analyze the equation.
The given equation: \[ (y'')^2 + (y')^3 = x \sin(y'), \] contains a non-polynomial term \( \sin(y') \). Hence, the degree is not defined. Step 3: Conclusion.
The degree is: \[ \boxed{\text{Not defined}}. \]
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