微分方程求解问题

wyh304

微分方程 a*y''+b*y^3=0    (y(0)=0, y'(0)=c)  y是关于x的函数，其中a,b,c是常数。 谁能帮我把这个方程解出来， 或者能够证明方程的解的周期是 T=2*pai/(c^2*b/a)^0.25  

hcui

assume y=Acos(wt+phi) then apply into original equation, you will find the period is correct or NOT.

wyh304

hcui 发表于 2012-6-18 23:48
assume y=Acos(wt+phi) then apply into original equation, you will find the period is correct or NOT.

why are you assuming y=Acos(wt+phi) which is not the solution of original equation.  Can you show me more details on how to prove the period. Thanks a lot.