Question

The order of differential equation $\frac{𝑑^3𝑦}{dx^3} + 2 \frac{𝑑^2𝑦}{dx^2} − 3 \frac{𝑑𝑦}{dx} + 6𝑥^4𝑦$ = 0 is _______.

Answer 1

Correct Answer: 3

The order of a differential equation is determined by the highest derivative present in the equation. Considering the given differential equation: $$\frac{d^3y}{dx^3} + 2\frac{d^2y}{dx^2} - 3\frac{dy}{dx} + 6x^4y = 0,$$ we observe the following derivatives: $\frac{d^3y}{dx^3}$, $\frac{d^2y}{dx^2}$, and $\frac{dy}{dx}$. The highest order derivative is $\frac{d^3y}{dx^3}$, which is the third derivative of y with respect to x. Hence, the order of this differential equation is 3. Now, we verify that this order fits within the provided range (3,3). Since the calculated order is 3, which matches the specified range, the solution is valid. Therefore, the order of the differential equation is 3.