Question
A curve passes through the point (0, 3) and has the property that the slope of the curve at every point p is twice the y-coordinate of p. what is the equation of the curve? (use x as the independent variable.)
Asked by: USER8679
209 Viewed
209 Answers
Answer (209)
You are given the separable differential equation
dy/dx = 2y
and the requirement that y=3 for x=0.
The solution is found as
∫(dy/y) = ∫(2dx)
ln(y) = 2x+c
Substituting the given point gives
ln(3) = 2·0 +c
So the equation can be written as
ln(y) = 2x+ln(3)
or
y = 3e^(2x)
dy/dx = 2y
and the requirement that y=3 for x=0.
The solution is found as
∫(dy/y) = ∫(2dx)
ln(y) = 2x+c
Substituting the given point gives
ln(3) = 2·0 +c
So the equation can be written as
ln(y) = 2x+ln(3)
or
y = 3e^(2x)