NDA 1 2024 Maths, question 71

Topic: Differential equations

Q71

Let $y_{1}(x)$ and $y_{2}(x)$ be two solutions of the differential equation $\frac{dy}{dx}=x$ . If $y_{1}(0)=0$ and $y_{2}(0)=4$ , then what is the number of points of intersection of the curves $y_{1}(x)$ and $y_{2}(x)$ ?

(a) No pointCorrect answer
(b) One point
(c) Two points
(d) More than two points

Solution.

Answer: (a) No point

Integrating the stated derivative gives y = x²/2 + C.
The two initial conditions give y₁ = x²/2 and y₂ = x²/2 + 4.
Their difference is constantly 4, so the curves do not intersect.