Let y = y 1 x and y = y 2 x be the solution curves the differential equation d y d x = y + 7 with initial…

Let y=y1x and y=y2x be the solution curves the differential equation dydx=y+7 with initial conditions y10=0 and y20=1 respectively. Then the curves y=y1x and y = y2x intersect at

  1. no point
  2. two points
  3. one point
  4. infinite number of points

Solution

We have been given thatdydx=y+7⇒dyy+7=dx

⇒ln|y+7|=x+c

⇒|y+7|=k.ex

⇒y=k·ex-7

⇒y10=0⇒k=7⇒y1x=7ex-1

⇒y20=1⇒1=k-7⇒8=k

⇒y2x=8ex-7

⇒y1x=y2x⇒8ex-7=7ex-7

Hence, No point of intersection.

This is the required option.

Asked in: JEE Main 2023 (13 Apr Shift 1)

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