If the order and the degree of the differential equation \(\left(\displaystyle\frac{dy}{dx}\right)^{\frac{1}{2}} = \left(\displaystyle\frac{d^2y}{dx^2}\right)^{\frac{1}{5}}\) are O and S respectively, then S − O is equal to
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → 0
The degree is defined only when the equation is a polynomial in the derivatives, so the fractional powers must be removed first. Raising both sides to the power 10 (the LCM of 2 and 5):
\( \displaystyle \left(\frac{dy}{dx}\right)^{5} = \left(\frac{d^2y}{dx^2}\right)^{2} \)
The highest derivative is \(\frac{d^2y}{dx^2}\), so the order is O = 2.
Its highest power is 2, so the degree is S = 2.
\(S - O = 2 - 2 = 0\)
Tip: Read the degree only after the equation is free of fractional powers of the derivatives; here the printed power \(\frac{1}{5}\) is not the degree.