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

• A. \(2,1\)
• B. \(2,3\)
• C. \(1,2\)
• D. \(3,2\)

Hint:

Remove the radicals by squaring, then read the highest derivative and its power.

Answer 1

The Correct Option is B

Step 1: Approach
Make the equation polynomial in $y'$ and $y''$ in two steps.

Step 2: Steps
Squaring removes the outer radical and the $\tfrac32$ power turns into $3$. The fraction $\dfrac1{(y')^2}$ is cleared by multiplying by $(y')^2$.

Step 3: Resulting form
$(y')^2+1=(y')^2(y'')^3$. It is a polynomial. The highest derivative is $y''$, giving order $2$, raised to power $3$, giving degree $3$.

Step 4: Answer
Option (B).

Final Answer:
After clearing the roots the highest derivative is of order 2 and has power 3, option (B). \[ \boxed{2,\ 3} \]