The sum of the order and degree of the differential equation \(2x^3\left(\displaystyle\frac{d^2y}{dx^2}\right)^4 + \displaystyle\frac{d^3y}{dx^3} + y = 0\) is :
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → 4
The order is the order of the highest derivative present. The degree is the power of that highest derivative, once the equation is a polynomial in the derivatives (here it already is).
The highest derivative is \(\frac{d^3y}{dx^3}\):
\(\text{order} = 3\)
It appears to the power 1:
\(\text{degree} = 1\)
\(\text{order} + \text{degree} = 3 + 1 = 4\)
Tip: The degree is the power of the highest-order derivative, not the largest power in the equation. The power 4 on \(\frac{d^2y}{dx^2}\) does not count here.