The solution of (d y)/(d x)+P(x) y=0, is

We have,

$\frac{d y}{d x}+P(x) y=0 \Rightarrow d y+P(x) y d x=0 \Rightarrow \frac{d y}{y}=-P(x) d x$

On integrating, we get

$\log y=\int-P(x) d x+\log C \Rightarrow y=C e^{\int-P d x}$