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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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