微分方程(1+y)dx-(1-x))dy=0

求通解
2025-03-10 14:59:25
推荐回答(1个)
回答1:

(1+y)dx-(1-x)dy=0
(1+y)dx=(1-x)dy
∫ [1/(1-x)] dx = ∫ [1/(1+y) ]dy
-ln|1-x|=ln|1+y|+c
ln|1-x||1+y|=c
(1-x)(1+y)=e^c=c
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