Нахождение отличные от тождественного нуля решения дифференциального уравнения, страница 5

((15929767251982789428336599799885/2535301200456458802993406410752*sin(pi*n)*n^2-5734161139222659/4503599627370496*sin(pi*n)+5734161139222659/4503599627370496*pi*n*cos(pi*n))/n^3*2^n-(27227927363807715762992813480013/2535301200456458802993406410752*sin(pi*n)*n^2-5734161139222659/4503599627370496*sin(pi*n)+5734161139222659/4503599627370496*pi*n*cos(pi*n))/n^3)/(2^(2*n)-1)  

Dn=subs(R1^n*R2^n*(bn1*R2^n-bn2*R1^n)/(R2^(2*n)-R1^(2*n)),[R1,R2],[1,2])  

Dn =

-1791925356007081/562949953421312*(2^n)^2*(-sin(pi*n)+pi*n*cos(pi*n))/n^2/(2^(2*n)-1)  

D0=subs((a01-a02)/(2*log(R1/R2)),[R1,R2],[1,2])  

D0 =

-10.0989  

Bn=subs((bn2*R2^n-bn1*R1^n)/(R2^(2*n)-R1^(2*n)),[R1,R2],[1,2])  

Bn =

(-1791925356007081/562949953421312*sin(pi*n)+1791925356007081/562949953421312*pi*n*cos(pi*n))/n^2/(2^(2*n)-1)  

Определим несколько первых слагаемых:

un=(r^n*An+Cn/(r^n))*cos(n*x)+(r^n*Bn+Dn/(r^n))*sin(n*x)  

un =

(r^n*((15929767251982789428336599799885/2535301200456458802993406410752*sin(pi*n)*n^2-5734161139222659/4503599627370496*sin(pi*n)+5734161139222659/4503599627370496*pi*n*cos(pi*n))/n^3*2^n-(27227927363807715762992813480013/2535301200456458802993406410752*sin(pi*n)*n^2-5734161139222659/4503599627370496*sin(pi*n)+5734161139222659/4503599627370496*pi*n*cos(pi*n))/n^3)/(2^(2*n)-1)+2^n*((27227927363807715762992813480013/2535301200456458802993406410752*sin(pi*n)*n^2-5734161139222659/4503599627370496*sin(pi*n)+5734161139222659/4503599627370496*pi*n*cos(pi*n))/n^3*2^n-(15929767251982789428336599799885/2535301200456458802993406410752*sin(pi*n)*n^2-5734161139222659/4503599627370496*sin(pi*n)+5734161139222659/4503599627370496*pi*n*cos(pi*n))/n^3)/(2^(2*n)-1)/(r^n))*cos(n*x)+(r^n*(-1791925356007081/562949953421312*sin(pi*n)+1791925356007081/562949953421312*pi*n*cos(pi*n))/n^2/(2^(2*n)-1)-1791925356007081/562949953421312*(2^n)^2*(-sin(pi*n)+pi*n*cos(pi*n))/n^2/(2^(2*n)-1)/(r^n))*sin(n*x)  

u1=subs(un,n,1)  

Warning: Reference to uninitialized variable r in sym/subs at line 118.

> In C:\PROGRAMM\MATLAB6p1\toolbox\symbolic\@sym\subs.m at line 118

Warning: Reference to uninitialized variable r in sym/subs at line 118.

> In C:\PROGRAMM\MATLAB6p1\toolbox\symbolic\@sym\subs.m at line 118

u1 =

(-1911387046407553/4503599627370496*r*pi-1911387046407553/2251799813685248*pi/r)*cos(x)+(-1791925356007081/1688849860263936*r*pi+1791925356007081/422212465065984*pi/r)*sin(x)  

u2=subs(un,n,2)  

Warning: Reference to uninitialized variable r in sym/subs at line 118.

> In C:\PROGRAMM\MATLAB6p1\toolbox\symbolic\@sym\subs.m at line 118

Warning: Reference to uninitialized variable r in sym/subs at line 118.

> In C:\PROGRAMM\MATLAB6p1\toolbox\symbolic\@sym\subs.m at line 118

u2 =

(5734161139222659/90071992547409920*r^2*pi+5734161139222659/22517998136852480*pi/r^2)*cos(2*x)+(1791925356007081/16888498602639360*r^2*pi-1791925356007081/1055531162664960*pi/r^2)*sin(2*x)  

u3=subs(un,n,3)  

Warning: Reference to uninitialized variable r in sym/subs at line 118.

> In C:\PROGRAMM\MATLAB6p1\toolbox\symbolic\@sym\subs.m at line 118

Warning: Reference to uninitialized variable r in sym/subs at line 118.

> In C:\PROGRAMM\MATLAB6p1\toolbox\symbolic\@sym\subs.m at line 118

u3 =

(-1911387046407553/121597189939003392*r^3*pi-1911387046407553/15199648742375424*pi/r^3)*cos(3*x)+(-1791925356007081/106397541196627968*r^3*pi+1791925356007081/1662461581197312*pi/r^3)*sin(3*x)  

u4=subs(un,n,4)  

Warning: Reference to uninitialized variable r in sym/subs at line 118.

> In C:\PROGRAMM\MATLAB6p1\toolbox\symbolic\@sym\subs.m at line 118

Warning: Reference to uninitialized variable r in sym/subs at line 118.

> In C:\PROGRAMM\MATLAB6p1\toolbox\symbolic\@sym\subs.m at line 118

u4 =

(5734161139222659/1224979098644774912*r^4*pi+5734161139222659/76561193665298432*pi/r^4)*cos(4*x)+(1791925356007081/574208952489738240*r^4*pi-1791925356007081/2243003720663040*pi/r^4)*sin(4*x)