The order and the degree of the differential equation \(\displaystyle\frac{d^4y}{dx^4} + \left(\frac{d^2y}{dx^2}\right)^3 + y = e^{x}\) are respectively
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 4 and 1
The order is the order of the highest derivative present, and the degree is the power of that highest derivative when the equation is a polynomial in the derivatives.
The highest derivative present is \(\frac{d^4y}{dx^4}\), so
\(\text{order} = 4\)
It appears with power 1 (the power 3 belongs to the lower derivative \(\frac{d^2y}{dx^2}\)), so
\(\text{degree} = 1\)