A curve passes through the point (0,3) and has the property that the slop of the curve at every point P is twice the y-coordinate of P. What is the equation of the curve y(x)=? Solution A curve passes through the point (0,3) and has the property that the slop of the curve at every point P is twice the y-coordinate of P. What is the equation of the curve y(x)=? slope = dy/dx = 2y dy/y = 2 dx take integration lny = 2x + C since it is passing through (0,3) ln3 = 2*0 + c C = ln3 lny = 2x + ln 3 y = 3 e^2x y(x) = 3 e^2x.