Re: [微方] 請教一題二階非線性ODE

[Frobenius (▽．(▽×▽φ)=0)]

※ 引述《doublewhi (whi)》之銘言：
: y'' + y^(3/2) = 0
: y(0)=0
: y'(0)=V0
: 目前試過降階...  但是出來的式子實在是積不出來= =
: 感謝~~

In[1]:= DSolve[{y''[t]+y[t]^(3/2)==0,y[0]==0},y[t],t]// FullSimplify

Out[1]:= Solve[t^2 == (Hypergeometric2F1[2/5, 1/2, 7/5, R[t]])^2 y[t]^2 /C[1]]

P.S. R[t] = (4 y[t]^(5/2))/(5 C[1])

By Mathematica 8.0

http://mathworld.wolfram.com/HypergeometricFunction.html

--
※ 發信站: 批踢踢實業坊(ptt.cc) 
◆ From: 118.168.122.118
推 doublewhi   :謝謝  我再看看