A curve passes through the point (0,5) 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?
Recall that the slope of the curve at a point
Therefore, by what has been given, we have,
This is a Separable Variable Type Diff. Eqn., and, to find its
General Solution, we integrate it termwise, and get,
Since, this curve passes through the point
Hence, the eqn of the curve is,