Question

Sketch the solution curves for y'=xy

How do I sketch this??? Where do I start?

Answer 1

You can separate the variables and integrate.

dy/dx = xy
dy/y = xdx
Integrate to get
log(y)+c = x²/2 (C=constant)
e^log(y)+c = e^{x^2/2}
e^cy = e^{x^2/2}
y = ke^{x^2/2} where k=e^-c
Now you can plot a family of curves for the solution y=f(x).