Calculus
posted by Emma on .
Sketch the solution curves for y'=xy
How do I sketch this??? Where do I start?

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^{c}y = 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).