The order and the degree of the differential equation
\(\displaystyle\frac{d^2y}{dx^2} = \left(1 + \frac{dy}{dx}\right)^{\frac{1}{2}}\)
respectively are:
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → order = 2, degree = 2
The highest derivative present is \(\frac{d^2y}{dx^2}\), so the order is 2.
The degree is read only when the equation is a polynomial in the derivatives. The power \(\frac{1}{2}\) must first be removed by squaring both sides:
\( \displaystyle \left(\frac{d^2y}{dx^2}\right)^2 = 1 + \frac{dy}{dx} \)
The highest-order derivative now appears with power 2, so the degree is 2.
Tip: Never read the degree from an equation with a fractional power or a root of a derivative; clear it first. Reading the power 1 of \(\frac{d^2y}{dx^2}\) straight from the printed form gives the wrong degree 1.