Question

The order and degree of the differential equation $\sqrt{1+\dfrac{1}{\left(\dfrac{dy}{dx}\right)^2}}=\left(\dfrac{d^2y}{dx^2}\right)^{\tfrac{3}{2}}$ are respectively

• A. $3,\ 2$
• B. $2,\ 3$
• C. $2,\ 2$
• D. $3,\ 3$

Hint:

Before finding degree, always remove radicals and fractions involving derivatives.

Answer 1

The Correct Option is B

Step 1: Removing radicals and fractions.
Square both sides: \[ 1+\frac{1}{\left(\frac{dy}{dx}\right)^2}=\left(\frac{d^2y}{dx^2}\right)^3 \]
Step 2: Identifying order.
The highest order derivative present is $\dfrac{d^2y}{dx^2}$. Hence, the order is $2$.
Step 3: Identifying degree.
The highest power of the highest order derivative is $3$. Hence, the degree is $3$.
Step 4: Conclusion.
The order and degree are $2$ and $3$ respectively.