If \(m\) and \(n\) are respectively the order and degree of the differential equation \(\left(\displaystyle\frac{d^2y}{dx^2}\right)^2+\left(\frac{dy}{dx}\right)^3+y=4x\), then the value of \(m + n\) is:
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 4
The order is the order of the highest derivative present, \(\frac{d^2y}{dx^2}\):
\(m = 2\)
The equation is a polynomial in the derivatives, so its degree is the power of the highest order derivative, \(\left(\frac{d^2y}{dx^2}\right)^2\):
\(n = 2\)
\(m + n = 2 + 2 = 4\)
Tip: The degree is the power of the highest order derivative only. The larger power 3 on \(\frac{dy}{dx}\) does not count.