(tanx)dy/dx=1+y求通解

题目

(tanx)dy/dx=1+y求通解

答案

tanx•dy/dx = 1 + y
dy/dx•1/(1 + y) = cotx
dy/(1 + y) = cotxdx
ln|1 + y| = ln|sinx| + lnC = ln|C•sinx|
1 + y = C•sinx
y = C•sinx - 1