求助二元四阶微分方程求解

bpzf

二元四阶微分方程如附件，怎么结果中有积分和复数啊？
后面是代码

1. omega := f*sin(Pi*m*x/a)*(sin(Pi*y/b))^2;
   
2. eq1 := E*((diff(diff(omega, y), x))^2-(diff(diff(omega, x), x))*(diff(diff(omega, y), y)));
   
3. eq2:=combine(eq1);
   
4. eq3 := diff(diff(diff(diff(F(x, y), x), x), x), x)+2*(diff(diff(diff(diff(F(x, y), y), y), x), x))+diff(diff(diff(diff(F(x, y), y), y), y), y);
   
5. pde := eq2 = eq3;
   
6. sol := pdsolve(pde,F(x,y));

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maplelab

最好用代码或者图片说明意图.

feiyuzhen

第二张图太小，不能说明问题

maplelab

截图真的很小,无法看清.

bpzf

顶起来，希望高手帮忙，谢谢

caoer

不是所有的pde都有解的，4阶2元出现复数很正常，君不见2元ODE在delta<0的情况。

bpzf

那后面那部分怎么是积分型式呢？

maplelab

用build选项尝试获取显式.

bpzf

各位，我已经把代码上传，希望大家帮帮忙

maplelab

9# bpzf

1. pdetest(sol, pde)

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解没有问题.

bpzf

哦，谢谢maplelab 了，我再看看

bpzf

为什么用显式的就计算不出来了，结果用pdetest检验不等于0？？？
omega := f*sin(Pi*m*x/a)*(sin(Pi*y/b))^2;

eq1 := E*((diff(diff(omega, y), x))^2-(diff(diff(omega, x), x))*(diff(diff(omega, y), y)));

eq2:=combine(eq1);

eq3 := diff(diff(diff(diff(F(x, y), x), x), x), x)+2*(diff(diff(diff(diff(F(x, y), y), y), x), x))+diff(diff(diff(diff(F(x, y), y), y), y), y);

pde := eq2 = eq3;

sol := pdsolve(pde, HINT = `+`, INTEGRATE, build)；