Question

Find an equation of the curve that passes through the point (0, 1) and whose slope at (x, y) is 5xy.

Answer 1

slope = dy/dx
\[\frac{dy}{dx} = 5xy\]
\[\frac{dy}{y}= 5x dx\]
integrate both sides
\[\ln y = (5/2) x^{2} +C\]
\[y = k e^{2.5x^{2}}\]
(k = e^C)
plug in given point to find "k"