Posted by Andres on Tuesday, October 11, 2011 at 8:15am.
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 y-intercept of y1 is (0,a), but that is also the y-intercept 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 y-intercept
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