Let y₁(x) and y₂(x) be two solutions of the differential equation d y d x =x . If y₁(0)=0 and y₂(0)=4 , then what is the number of points of intersection of curves y₁(x) and y₂(x) ?

Step-by-step solution

Given, D.E. d y d x =x aligned & d y & = x d x & y & = x^2 2 +c aligned y₁(x)= x^2 2 +c₁ ...(i) and y₂(x)= x^2 2 +c₂ ...(ii) For y₁(0)=0 in equation (i) 0=0+c₁ c₁=0 y₁(x)= x^2 2 ...(iii) For y₂(0)=0 4=0+c₂ [ From (iii) ] For, c₂=4 y₂(x)= x^2 2 +4 ...(iv) For number of points of intersection for y₁(x) and y₂(x) solving (iii) and (iv) x^2 2 = x^2 2 +4 (not possible) as 0 4 Hence, no point of intersection.