[交流] 师兄师姐们，帮小弟看看这个 Laplace变换后的二阶常微分方程怎么解啊已有3人参与

4楼: Originally posted by 吕春莹 at 2014-07-20 11:09:10
但是，反过来 ans=a*diff(Y,x,2)-diff(Y,x)/x-s*Y

ans =

a*(C3*x^((a + 1)/(2*a))*((s^(1/2)*((besselk(1 - (a + 1)/(2*a), -(s^(1/2)*x)/a^(1/2))*((a + 1)/(2*a) - 1))/x + (s^(1/2)*besselk(-(a + 1)/( ...

6楼: Originally posted by 月只蓝 at 2014-07-20 16:21:44
结果见附图。

附图1.png

7楼: Originally posted by 吕春莹 at 2014-07-20 19:08:10
我在3楼写的是用matlab算
syms a s y x
Y=dsolve('a*D2y-Dy/x-s*y=0','x')

解析解是
Y =
C3*x^((a + 1)/(2*a))*besselk(-(a + 1)/(2*a), -(s^(1/2)*x)/a^(1/2)) + (C2*x^((a + 1)/(2*a))*besseli(-(a + 1) ...

11楼: Originally posted by 月只蓝 at 2014-07-20 20:00:59
安装包小木虫里就有的吧。...

6楼: Originally posted by 月只蓝 at 2014-07-20 16:21:44
结果见附图。

附图1.png

4楼: Originally posted by 吕春莹 at 2014-07-20 11:09:10
但是，反过来 ans=a*diff(Y,x,2)-diff(Y,x)/x-s*Y

ans =

a*(C3*x^((a + 1)/(2*a))*((s^(1/2)*((besselk(1 - (a + 1)/(2*a), -(s^(1/2)*x)/a^(1/2))*((a + 1)/(2*a) - 1))/x + (s^(1/2)*besselk(-(a + 1)/( ...

19楼: Originally posted by 月只蓝 at 2014-07-21 16:54:58
Y(0)=1;Y(1)=2的条件的话，就是边值问题，哪有（或者很难）有解析解。
Y(0)=,Y'(0)= 的条件是初值问题，可以试着找解析解。...

20楼: Originally posted by 吕春莹 at 2014-07-21 18:52:48
你的方程x在分母位置，x不可以为0，所以你的条件Y（0）=1需要修改
用matlab解方程组用
x=1;y1=subs(Y);
x=2;y2=subs(Y);
= solve（‘y1=1’，‘y2=2’）
解出C1，C2，你再代回去
y=subs(Y)
x=
plot(Y)
给 ...