find a function f given that (1) the slope of the tangent line to graph of f at any point P(x,y) is given by dy/dx=3xy and (2) the graph of f passes through the point (0,2)

Answer 1

dy/dx = 3xy
dy/y = 3x dx
ln y = 3x^2/2+c
y = Ce^3x^2/2

2 = Ce^0
C = 2

y = 2e^(3x^2/2)
y' = 2e^(3x^2/2)*(3x)
= 3xy