方法如下,
请作参考:
y(0) =1
p(x) =tanx
e^[∫ p(x) dx] = 1/cosx
y'.cotx +y = 2
y' +(tanx)y = 2tanx
(1/cosx). [y' +(tanx)y] = 2tanx .(1/cosx)
d/dx ( y/cosx) = 2sinx/(cosx)^2
y/cosx =∫ [2sinx/(cosx)^2] dx
=2/cosx +C
y = 2 +C.cosx
y(0) =1
1=2+C
C=-1
ie
y = 2 -cosx