Logaritm problem (inom en differential ekvation)

$ln\lvert 1+y\lvert = ln\lvert x\lvert + C_1 \implies e^{ln\lvert 1+y \lvert} = e^{ln\lvert x \lvert + C_1} \implies \lvert 1+y \lvert = e^{C_1}\lvert x \lvert \implies 1+y = C_2x$