Posted by Andres on Tuesday, October 11, 2011 at 8:15am.
Suppose Y1 is a function of x which dy1/dx=3y1. Suppose y2 is a function of x which dy2/dx=8x+5. If the graphs of y1 and y2 have the same yintercept and they intersect at x=2, then determine the value of the yintercept.

Calc  Reiny, Tuesday, October 11, 2011 at 8:44am
if dy1/dx = 3y1
then y1 = ae^(3x) , where a is a constant, a≠ 0
(check: dy1/dx = 3a(e^(3x)) = 3y1 )
if dy2/dx = 8x + 5
then y2 = 4x^2 + 5x + c
the yintercept of y1 is (0,a), but that is also the yintercept of y2
so in y2:
a = 0 +0 + c
a = c
when x=2
y1 = a(e^6) , y2 = 16+10+c = c + 26
but a=c, so
a(e^6) = a+26
a(e^6)  a = 26
a(e^6  1) = 26
a = 26/(e^6  1) , which would be the yintercept
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