calculus

if dy/dx= (1+lnx)y and if y=1 when x=1, then y=

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  1. dy/dx= (1+lnx)y --->

    dy/y = (1 + ln(x)) dx --->

    ln(y) = x ln(x) + c

    Boundary condition:

    y=1 when x=1 ---> c = 0

    y = exp(x ln(x)) = x^x

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