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Two solutions of a first order equation with different starting values: how many points they meet

This type of question, asked 2 times: 27 Jul 2022, 13 Apr 2023. All 2 questions below, oldest first.

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  1. Question 1

    27 Jul 2022

    70
    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\frac{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

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  2. Question 2

    13 Apr 2023

    79
    Let y=y1(x)y =y_{1}(x) and y=y2(x)y =y_{2}(x) be the solution curves of the differential equation dydx=y+7\frac{dy}{dx}= y + 7 with initial conditions y1(0)=0,y2(0)=1y_{1}(0) = 0,y_{2}(0) = 1 respectively. Then the curves y=y1(x)y =y_{1}(x) and y=y2(x)y =y_{2}(x) intersect at

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