隐函数求导问题

scott198510

想问问 群里的虾米们 关于隐函数求导问题：
clc;clear ;
CO=0.28706;  %常数部分
C1=0.06302;
C2=-0.40664;
C3=1.07551;
C4=-1.22462;
C5=0.8041;
B0=309.06;
B1=-1053.97;
B2=8436.26;
B3=-30348.48;
B4=50123.55;
B5=-30809.65;
D0=3.005;
D1=8.395;
D2=-43.430;
D3=120.421;
D4=-173.53;
D5=96.841;
E0=41.270;
E1=-152.569;
E2=1249.11;
E3=-4553.79;
E4=7588.14;
E5=-4692.13;
F0=0.0937;
F1=-0.1838;
F2=0.94688;
F3=-2.64259;
F4=3.83782;
F5=-2.05703;   %常数部分
syms Y x z R T  %字符定义
% Y=6.56*1e-5 ;
Y=exp(E0+E1*x+E2*(x^2)+E3*(x^3)+E4*(x^4)+E5*(x^5))*...
    ((sinh(F0+F1*x+F2*(x^2)+F3*(x^3)+F4*(x^4)+F5*(x^5))*z)...
    ^(D0+D1*x+D2*(x^2)+D3*(x^3)+D4*(x^4)+D5*(x^5)))*...
    exp((B0+B1*x+B2*(x^2)+B3*(x^3)+B4*(x^4)+B5*(x^5))/R/T);
%%%现在对y 求导 得到全微分方程
syms dy
syms dx dz
dy = diff(Y,x)*dx + diff(Y,z)*dz
经过上述求导后得到如下：
dy =

((-5368044465221009/35184372088832+5493643877485117/2199023255552*x-15020835166350213/1099511627776*x^2+8343248163192177/274877906944*x^3-25795257470183015/1099511627776*x^4)*exp(4127/100-5368044465221009/35184372088832*x+5493643877485117/4398046511104*x^2-5006945055450071/1099511627776*x^3+8343248163192177/1099511627776*x^4-5159051494036603/1099511627776*x^5)*(-sinh(-937/10000+919/5000*x-2959/3125*x^2+1487645917411625/562949953421312*x^3-4321001180478759/1125899906842624*x^4+2316009885372483/1125899906842624*x^5)*z)^(601/200+1679/200*x-4343/100*x^2+8473874542618477/70368744177664*x^3-17353/100*x^4+96841/1000*x^5)*exp((15453/50-4635409081308283/4398046511104*x+4637882982470779/549755813888*x^2-8342126661331845/274877906944*x^3+3444464128150733/68719476736*x^4-4234446052838605/137438953472*x^5)/R/T)+exp(4127/100-5368044465221009/35184372088832*x+5493643877485117/4398046511104*x^2-5006945055450071/1099511627776*x^3+8343248163192177/1099511627776*x^4-5159051494036603/1099511627776*x^5)*(-sinh(-937/10000+919/5000*x-2959/3125*x^2+1487645917411625/562949953421312*x^3-4321001180478759/1125899906842624*x^4+2316009885372483/1125899906842624*x^5)*z)^(601/200+1679/200*x-4343/100*x^2+8473874542618477/70368744177664*x^3-17353/100*x^4+96841/1000*x^5)*((1679/200-4343/50*x+25421623627855431/70368744177664*x^2-17353/25*x^3+96841/200*x^4)*log(-sinh(-937/10000+919/5000*x-2959/3125*x^2+1487645917411625/562949953421312*x^3-4321001180478759/1125899906842624*x^4+2316009885372483/1125899906842624*x^5)*z)+(601/200+1679/200*x-4343/100*x^2+8473874542618477/70368744177664*x^3-17353/100*x^4+96841/1000*x^5)*cosh(-937/10000+919/5000*x-2959/3125*x^2+1487645917411625/562949953421312*x^3-4321001180478759/1125899906842624*x^4+2316009885372483/1125899906842624*x^5)*(919/5000-5918/3125*x+4462937752234875/562949953421312*x^2-4321001180478759/281474976710656*x^3+11580049426862415/1125899906842624*x^4)/sinh(-937/10000+919/5000*x-2959/3125*x^2+1487645917411625/562949953421312*x^3-4321001180478759/1125899906842624*x^4+2316009885372483/1125899906842624*x^5))*exp((15453/50-4635409081308283/4398046511104*x+4637882982470779/549755813888*x^2-8342126661331845/274877906944*x^3+3444464128150733/68719476736*x^4-4234446052838605/137438953472*x^5)/R/T)+exp(4127/100-5368044465221009/35184372088832*x+5493643877485117/4398046511104*x^2-5006945055450071/1099511627776*x^3+8343248163192177/1099511627776*x^4-5159051494036603/1099511627776*x^5)*(-sinh(-937/10000+919/5000*x-2959/3125*x^2+1487645917411625/562949953421312*x^3-4321001180478759/1125899906842624*x^4+2316009885372483/1125899906842624*x^5)*z)^(601/200+1679/200*x-4343/100*x^2+8473874542618477/70368744177664*x^3-17353/100*x^4+96841/1000*x^5)*(-4635409081308283/4398046511104+4637882982470779/274877906944*x-25026379983995535/274877906944*x^2+3444464128150733/17179869184*x^3-21172230264193025/137438953472*x^4)/R/T*exp((15453/50-4635409081308283/4398046511104*x+4637882982470779/549755813888*x^2-8342126661331845/274877906944*x^3+3444464128150733/68719476736*x^4-4234446052838605/137438953472*x^5)/R/T))*dx+exp(4127/100-5368044465221009/35184372088832*x+5493643877485117/4398046511104*x^2-5006945055450071/1099511627776*x^3+8343248163192177/1099511627776*x^4-5159051494036603/1099511627776*x^5)*(-sinh(-937/10000+919/5000*x-2959/3125*x^2+1487645917411625/562949953421312*x^3-4321001180478759/1125899906842624*x^4+2316009885372483/1125899906842624*x^5)*z)^(601/200+1679/200*x-4343/100*x^2+8473874542618477/70368744177664*x^3-17353/100*x^4+96841/1000*x^5)*(601/200+1679/200*x-4343/100*x^2+8473874542618477/70368744177664*x^3-17353/100*x^4+96841/1000*x^5)/z*exp((15453/50-4635409081308283/4398046511104*x+4637882982470779/549755813888*x^2-8342126661331845/274877906944*x^3+3444464128150733/68719476736*x^4-4234446052838605/137438953472*x^5)/R/T)*dz

令dy=0,式子里面只有x,z,dx,dz 现在想对方程变形求出dz/dx的表达式，式子里面右边是含有ｘ，ｚ的表达式，不需要求出积分，改怎么求法呢，我用dsolve　函数得不到要求的结果，哪位大虾米指点一下

scott198510

1# scott198510


自己解决了哈，
fx=diff(Y,x)
fz=diff(Y,z)
% 令dy=0 即 diff(Y,x)*dx + diff(Y,z)*dz =0
dz/dx= - fx/fz