Question

如何求微分方程通解

给个详细过程，刚开始学，搞不太懂

Answer 1

xy'-ylny =0
xy'=ylny
∫dy/(ylny) = ∫dx/x
ln|lny| = ln|x| +C'
lny =e^C'. x
y = e^[e^C'. x]
=C.e^x

追问

第二部到第三部看不太懂阿

追答

xy'-ylny =0
xy'=ylny

x.dy/dx =ylny

∫dy/(ylny) = ∫dx/x

∫ dlny/lny =∫dx/x

ln|lny| = ln|x| +C'
lny =e^C'. x
y = e^[e^C'. x]
=C.e^x

Answer 2