求dy/dx-2y=1的通解

题目

求dy/dx-2y=1的通解

答案

dy/dx-2y=1
∫dy/(1+2y) =∫dx
(1/2)ln|1+2y| = x + C1
ln|1+2y| = 2(x+C1)
1+2y = e^[2(x+C1)]
y = (1/2)(e^[-1+-2(x+C1)] )
=(1/2)( -1+Ce^(-2x) )