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← JEE Main 2022 · 27 Jul · Shift 1
MathematicsSingle correct+4 / -1Question 10 of 90

JEE Main 2022 · 27 Jul · Shift 1, Mathematics question 10

Let y=y1(x)y=y_1(x) and y=y2(x)y=y_2(x) be two distinct solutions of the differential equation dydx=x+y\dfrac{dy}{dx}=x+y, with y1(0)=0y_1(0)=0 and y2(0)=1y_2(0)=1 respectively. Then, the number of points of intersection of y=y1(x)y=y_1(x) and y=y2(x)y=y_2(x) is

Choose one option
Answer and worked solution

Official answer: A

Solve. y=Cex−x−1y=Ce^x-x-1: y1=ex−x−1y_1=e^x-x-1, y2=2ex−x−1y_2=2e^x-x-1.

Equal only if ex=2exe^x=2e^x, which never happens: 0 points.

(A)