I \(\heartsuit\) Substitution!

Calculus Level 5

\[\frac{dy}{dx}+\frac{y}{x}=\ln x \times y^{2}\]

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

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

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