Non-homogeneous and linear-differential-equation solutions (update:13-07-07)
Keine Lizenz
DESCRIPTION;
This program is a running module for homsolution.m Matlab-functions. Also, differential non-homogeneous or homogeneous equations are solution possible the Matlab&Mapple Dsolve.m&desolve main-functions. But;
EXAMPLE;
[1]--+---Sometime mapple function is produce more short solution
|--- My function's solution:
[ R^4-4*R^3 ]*(y) = [5 ]
y = [ +exp^(4x).(C4)+exp^(0x).(C1+C2*x^1+C3*x^2) ]g + [-5/24*x^3-5/32*x^2-5/64*x-5/256 ]s
Generally solution Special solution
#### true ##### #### true #####
|
|--- Mapple's desolve function solution:
Dsolve('D4y-4*D3y-5=0','x')
ans =1/64*exp(4*x)*C1-5/24*x^3+1/2*C2*x^2+C3*x+C4
y= 1/64*exp(4*x)*C1 + 1/2*C2*x^2 + C3*x + C4 - 5/24*x^3
Generally solution Special solution (more short)
#### true ##### #### true #####
[2]---+---Matlab's Dsolve.m function is depend be selected input-veriables string character
|
|--- My function's solution:
>> homsolution([(R^4-16)^5*(R^2+1)*(R/(R^2+R+1))^2, x^20+x^10+sin(x)],0)
where R=[d/dx] and [f(R)].y = Q(x,y) differential equation solution
____Equation [1]
[ (R^4-16)^5*(R^2+1)*R^2/(R^2+R+1)^2 ]*(y) = [x^20+x^10+sin(x) ]
y= [ +exp^(-2x).(C20+C21*x^1+C22*x^2+C23*x^3+C24*x^4)+exp^(2ix)+ ...]g+ [ ...1/1518750*x*cos(x)^6+ ...]s
|
|--- Mapple's desolve function solution:
Dsolve('((Dy)^4-16)^5*((Dy)^2+1)*(Dy)^2/((Dy)^2+Dy+1)^2-(x^20+x^10+sin(x))=0','x')
(I don't advise , don't try this module, non-solution )
[3]---+---Sub-function running speed (for running 29-examples)
if you hide homsolution.m-lines(68,69,155,156) as fprintf,disp etc.. command then
My function is 1.602342 second (tic-toc & profiler control)
Matlab function is 1.094779 second
ALGORITHM;
--+--if Q(x,y)<> 0 than special solution
root value root-order degree
r1=R1 n1
r2=R2 n2
..... ....
rn=Rn nn
|---+---if root value = real
|
|----+---[max real root order degree]
else
|
Solution=1/[R-small root(1)]...
1/[R-small root(2)]...
1/[R-small root(n)]*[Q(x,y] (**)
where all step is first-order degree linear diff. equ. sol.
|---+---if root value = complex
|
|----+---[max complex root order degree]
else
|
Solution=1/[R-small root(1)]...
1/[R-small root(2)]...
1/[R-small root(n)]*[Q(x,y] (**)
where all step is first-order degree linear diff. equ. sol.
SYNTAX:
syntax.input : solution=regsolution.ouput (differential main function solution)
syntax.output: regsolt =conforming roots values for special solutions
EXAMPLE:
[ (R-2)^2*(R^2+1)^2*(R-1)^2 ]*(y) = [x^8 ]
Solution=
1.0000 2.0000
2.0000 2.0000
0 + 1.0000i 2.0000
0 - 1.0000i 2.0000
regsolt =
1.0000 firstly real roots
1.0000
2.0000
2.0000 --->look ALGORITHM<---
0 - 1.0000i
0 - 1.0000i
0 + 1.0000i secondly imaginer roots
0 + 1.0000i
Solution=[1/(R-1)][1/(R-1)][1/(R-2)][1/(R-2)][1/(R+sqrt(-1))] [1/(R+sqrt(-1))][1/(R-sqrt(-1))][1/(R-sqrt(-1))][ Q(x,y) ]
Zitieren als
Ali OZGUL (2024). Non-homogeneous and linear-differential-equation solutions (update:13-07-07) (https://www.mathworks.com/matlabcentral/fileexchange/15514-non-homogeneous-and-linear-differential-equation-solutions-update-13-07-07), MATLAB Central File Exchange. Abgerufen .
Kompatibilität der MATLAB-Version
Plattform-Kompatibilität
Windows macOS LinuxTags
Quellenangaben
Inspiriert von: Jean Le Rand D'Alambert Reduction Method (update:22-06-07), First-Order Degree Linear Differential Equations (Integration factor Ig=x^a*y^b) (Update: 23-06-07), Homogen Differential Equations Solving (update:27-06-07)
Community Treasure Hunt
Find the treasures in MATLAB Central and discover how the community can help you!
Start Hunting!Live Editor erkunden
Erstellen Sie Skripte mit Code, Ausgabe und formatiertem Text in einem einzigen ausführbaren Dokument.
html/
Version | Veröffentlicht | Versionshinweise | |
---|---|---|---|
1.0.0.0 | Updated regsolution.m file |