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Calculus Level 4

dydx+yx=lnx×y2\frac{dy}{dx}+\frac{y}{x}=\ln x \times y^{2}

Let y=f(x)y=f(x) be a solution to the above differential equation such that f(1)=1f(1)=1.

Given that f(x)=axb(clndx)f(x)=\dfrac{a}{x^{b}\left(c-\ln^{d}x\right)} for positive real numbers a,b,ca,b,c and dd, find a+b+c+da+b+c+d.

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