Question

如何用MATLAB解

Answer 1

dsolve('D2y/(sqrt(1+(Dy)^2)/2)=1/(1-x)')

结果是 C26 - cosh((C24 + t/2 - C24*x)/(x - 1))*(2*x - 2)

用mathematica做，DSolve[(1 - x) D[y[x], {x, 2}] == Sqrt[1 + (D[y[x], x])^2]/5, y[x], x]，

结果是
{{y[x] ->
C[2] - 1/8 (5 - 5 x)^(4/5) Cosh[C[1]] +
1/12 (5 - 5 x)^(6/5) Cosh[C[1]] -
1/8 (5 - 5 x)^(4/5) Sinh[C[1]] - 1/12 (5 - 5 x)^(6/5) Sinh[C[1]]}}

Answer 2

符号解：
dsolve('(1-x)*D2y=sqrt(1+(Dy)^2)/5','x')

数值解：
clear;clc
[x,y]=ode45('pizid',[2 10],[1;0]);
plot(x,y)
------------------------
function dy=pizid(x,y)
dy=[y(2);sqrt(1+y(2)^2)/(5*(1-x))];