1。xdy-ylnydx=0 解：∵xdy-ylnydx=0 ==>xdy=ylnydx ==>dy/(ylny)=dx/x ==>d(lny)/lny=dx/x ==>ln│lny│=ln│x│+ln│C│ (C是积分常数) ==>lny=Cx ==>y=e^(Cx) ∴原微分方程的通解是y=e^(Cx) (C是积分常数) 2。y'=1+y^2-2x-2xy^2,y(0)=0 解：∵y'=1+y-2x-2xy ==>y'=1-2x+y(1-2x) ==>y'=(1-2x)(1+y) ==>dy/(1+y)=(1-2x)dx ==>arctany=x-x+C (C是积分常数) ==>y=tan(x-x+C) 又y(0)=0，则把它带入上式，得0=tanC,即C=0 ∴原微分方程的解是y=tan(x-x)
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