Match the LIST-I with LIST-II
| LIST-I | LIST-II | ||
| Differential equation | Sum of the order and the degree of the differential equation | ||
| A. | \( \displaystyle\frac{d}{dx}\left(\displaystyle\frac{dy}{dx}\right)=1 \) | I. | 2 |
| B. | \( 4+\left(\displaystyle\frac{dy}{dx}\right)^4=7\left(\displaystyle\frac{d^2y}{dx^2}\right)^3 \) | II. | 3 |
| C. | \( x^3\left(\displaystyle\frac{d^2y}{dx^2}\right)^2+x\left(\displaystyle\frac{dy}{dx}\right)^4+1=0 \) | III. | 5 |
| D. | \( \displaystyle\frac{dy}{dx}=x^4e^{-3y} \) | IV. | 4 |
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → A-II, B-III, C-IV, D-I
The order is the order of the highest derivative; the degree is the power of that highest derivative when the equation is a polynomial in its derivatives. The powers of lower derivatives do not count.
A. \( \frac{d}{dx}\left(\frac{dy}{dx}\right)=1 \)
This matches II. 3.
\( \displaystyle \frac{d^2y}{dx^2}=1:\ \text{order }2,\ \text{degree }1,\ \text{sum }3 \)
B. \( 4+\left(\frac{dy}{dx}\right)^4=7\left(\frac{d^2y}{dx^2}\right)^3 \)
This matches III. 5.
\( \displaystyle \text{order }2,\ \text{degree }3,\ \text{sum }5 \)
C. \( x^3\left(\frac{d^2y}{dx^2}\right)^2+x\left(\frac{dy}{dx}\right)^4+1=0 \)
This matches IV. 4.
\( \displaystyle \text{order }2,\ \text{degree }2,\ \text{sum }4 \)
D. \( \frac{dy}{dx}=x^4e^{-3y} \)
This matches I. 2. The term \( e^{-3y} \) involves y, not a derivative, so the equation is still a polynomial in \( \frac{dy}{dx} \).
\( \displaystyle \text{order }1,\ \text{degree }1,\ \text{sum }2 \)
So the matching is A-II, B-III, C-IV, D-I.