The order and degree of the differential function
\[
\left[ 1 + \left( \frac{dy}{dx} \right)^2 \right]^5 = \frac{d^2y}{dx^2}
\]
Show Hint
To determine the order, identify the highest derivative in the equation. The degree refers to the power of the highest order derivative after it has been made free from radicals or fractions.
The given differential equation is:
\[
\left[ 1 + \left( \frac{dy}{dx} \right)^2 \right]^5 = \frac{d^2y}{dx^2}
\]
To find the order and degree, we need to identify the highest derivative and the power of the highest order derivative.
- The highest derivative present in the equation is \( \frac{d^2y}{dx^2} \), which is the second derivative of \(y\). Therefore, the order of the differential equation is 2.
- The highest power of the highest derivative is 1 in the term \( \frac{d^2y}{dx^2} \), meaning the degree is 2.
Thus, the order is 2 and the degree is 2.
