Question

For the differential equation [1 + $(\frac {dy}{dx})^2$]5/2 = 8 $(\frac {d^2y}{dx^2})$ has the order and degree_________respectively.

• A. 2 and 6
• B. 2 and 3
• C. 2 and 2
• D. 2 and 1

Answer 1

Answer: (C)

2 and 2

Answer 2

The given differential equation is [1 + $(\frac {dy}{dx})^2$]5/2 = 8$(\frac {d^2y}{dx^2})$.
The highest order derivative in the equation is the second derivative, $(\frac {d^2y}{dx^2})$. Therefore, the order of the differential equation is 2.
Next, we need to determine the degree of the differential equation, which is the highest power of the derivative. In this case, the second derivative appears inside the square root [1 + $(\frac {dy}{dx})^2$]5/2. The highest power of the derivative is 2 raised to the power of $(\frac {5}{2})$, which is (25/2). Therefore, the degree of the differential equation is 2.
Hence, the order and degree of the given differential equation are 2 and 2, respectively.
The correct option is (C) 2 and 2.