Question

The order and degree of the differential equation \(\sqrt{⎷1+\frac{1}{(\frac{dy}{dx})^2}} = (\frac{d^2y}{dx^2})^{\frac{3}{2}}\) are \(\ldots\)

• A. Order 2, Degree 3
• B. Order 2, Degree 2
• C. Order 3, Degree 3
• D. Order 3, Degree 2

Hint:

Remove the radicals and fractions so that all derivatives appear as polynomials, then read off the order and degree.

Answer 1

The Correct Option is A

Step 1: Find the highest derivative:
Only $y'$ and $y''$ occur. The highest is $y''$, so order $= 2$.

Step 2: Clear fractional powers:
Square both sides: $1 + (y')^{-2} = (y'')^3$. Multiply by $(y')^2$ to remove the negative power: $(y')^2 + 1 = (y')^2 (y'')^3$.

Step 3: Read the degree:
The exponent on $y''$ is 3, and no fractions or radicals remain. So degree $= 3$.
Order 3 is impossible because there is no $y'''$.

Final Answer:
Order 2, degree 3, option (A). \[ \boxed{\text{Order 2, Degree 3 (A)}} \]