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.)
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)
