Question:
The order and degree of the differential equation \(\sqrt{⎷1+\frac{1}{(\frac{dy}{dx})^2}} = (\frac{d^2y}{dx^2})^{\frac{3}{2}}\), respectively are
The order and degree of the differential equation \(\sqrt{⎷1+\frac{1}{(\frac{dy}{dx})^2}} = (\frac{d^2y}{dx^2})^{\frac{3}{2}}\), respectively are
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Remove the radicals by squaring, then read the highest derivative and its power.
Updated On: Oct 1, 2026
- \(2,1\)
- \(2,3\)
- \(1,2\)
- \(3,2\)
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The Correct Option is B
Solution and Explanation
Step 1: Understanding the Concept
Order is the order of the highest derivative. Degree is the power of that highest derivative after the equation is made a polynomial in the derivatives (free of fractional powers and roots).
Step 2: Remove the roots
\[ \sqrt{1+\frac{1}{(y')^2}}=(y'')^{3/2} \]
Square both sides:
\[ 1+\frac{1}{(y')^2}=(y'')^3 \]
Multiply by \((y')^2\):
\[ (y')^2+1=(y')^2(y'')^3 \]
Step 3: Read off
The highest derivative is \(y''\), so the order is 2. Its power is 3, so the degree is 3.
Step 4: Conclusion
The order and degree are 2 and 3, option (B).
Final Answer:
After clearing the roots the highest derivative is of order 2 and has power 3, option (B). \[ \boxed{2,\ 3} \]
Order is the order of the highest derivative. Degree is the power of that highest derivative after the equation is made a polynomial in the derivatives (free of fractional powers and roots).
Step 2: Remove the roots
\[ \sqrt{1+\frac{1}{(y')^2}}=(y'')^{3/2} \]
Square both sides:
\[ 1+\frac{1}{(y')^2}=(y'')^3 \]
Multiply by \((y')^2\):
\[ (y')^2+1=(y')^2(y'')^3 \]
Step 3: Read off
The highest derivative is \(y''\), so the order is 2. Its power is 3, so the degree is 3.
Step 4: Conclusion
The order and degree are 2 and 3, option (B).
Final Answer:
After clearing the roots the highest derivative is of order 2 and has power 3, option (B). \[ \boxed{2,\ 3} \]
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