The sum of order and degree of the differential equation \(\left(x^2\displaystyle\frac{d^2y}{dx^2}\right)^{3/4}= 5\left(\frac{dy}{dx}\right)^2- 3\) is equal to
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 5
The degree is defined only when the equation is a polynomial in the derivatives, so the power \(\frac{3}{4}\) must be removed first. Raising both sides to the power 4:
\( \displaystyle \left(x^2\frac{d^2y}{dx^2}\right)^{3} = \left(5\left(\frac{dy}{dx}\right)^2 - 3\right)^{4} \)
The highest derivative is \(\frac{d^2y}{dx^2}\), so the order is 2.
The power of \(\frac{d^2y}{dx^2}\) is now 3, so the degree is 3.
\(2 + 3 = 5\)