# I $$\heartsuit$$ Substitution!

Calculus Level 4

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

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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