How to solve $\left| \dfrac{dy}{dx}\right|+|y|=0$, $y(0)=1$?

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How can I solve the differential equation $\left| \dfrac{dy}{dx}\right|+|y|=0$, $y(0)=1$?.
Is it possible to solve
$|x|=\begin{cases} x, & x\geq 0\\ -x, & x<0 \end{cases}$.

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Come on, you have the sum of two positive functions which is equal to 0...