Calculus

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Sketch the solution curves for y'=xy

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

• Calculus -

You can separate the variables and integrate.
dy/dx = xy
dy/y = xdx
Integrate to get
log(y)+c = x²/2 (C=constant)
elog(y)+c = ex^2/2
ecy = ex^2/2
y = kex^2/2 where k=e-c
Now you can plot a family of curves for the solution y=f(x).

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