求各位朋友看一下这个问题.
请大家帮忙求解一下这个微分方程。d2y/d2x^2+1/x*dy/dx+1*(1-c2*x^2)^2-c3^2-c4^2/x^2]*y=0
直接利用dsolve解这个方程，得到的是非解析的解，有没有其它的方法求解此方程。
>> syms c1 c2 c3 c4 x y
>> Sy=dsolve('D2y+Dy/x+(c1*(1-c2*x^2)^2-c3^2-c4^2/x^2)*y=0','x')
Warning: Compact, analytic solution could not be found.
It is recommended that you apply PRETTY to the output.
Try mhelp dsolve, mhelp RootOf, mhelp DESol, or mhelp allvalues
for more information.
> In F:\MATLAB6p1\toolbox\symbolic\dsolve.m at line 299
Sy =
DESol({x^2*diff(Y(x),`$`(x,2))+x*diff(Y(x),x)+(c1*x^2-2*c1*x^4*c2+c1*x^6*c2^2-c3^2*x^2-c4^2)*Y(x)},{Y(x)})
>> pretty(Sy)
/ 2 \
2 |d | /d \
DESol({x |--- Y(x)| + x |-- Y(x)|
| 2 | \dx /
\dx /
2 4 6 2 2 2 2
+ (c1 x - 2 c1 x c2 + c1 x c2 - c3 x - c4 ) Y(x)}, {Y(x)})
>>
[ 本帖最后由 ChaChing 于 2010-6-14 00:30 编辑 ] <P>晕，没见过这种啊！不懂这个，不过我机子上是这样的：<br>>> syms c1 c2 c3 c4 x y <br><br>>> Sy=dsolve('D2y+Dy/x+(c1*(1-c2*x^2)^2-c3^2-c4^2/x^2)*y=0','x')<br><br>Sy =<br><br>DESol({diff(_Y(x),$(x,2))+1/x*diff(_Y(x),x)+(c1*(1-c2*x^2)^2-c3^2-c4^2/x^2)*_Y(x)},{_Y(x)})<br>>> pretty(Sy)<br> <br> d<br> / 2 \ -- _Y(x) / 2\<br> |d | dx | 2 2 2 c4 |<br>DESol({|--- _Y(x)| + -------- + |c1 (1 - c2 x )- c3- ---| _Y(x)},<br> |2 | x | 2 |<br> \dx / \ x/</P>
<P> {_Y(x)})</P>
[此贴子已经被作者于2006-5-29 10:42:35编辑过]
这个可能是你matlab 版本问题，如果是matlab 7不会出现LZ的问题。<BR>正如2楼所言。
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