First-Order Degree Linear Differential Equations (Integration factor Ig=x^a*y^b) (Update: 23-06-07)
Updated 25 Jun 2007
First-order-degree linear differential and non-homogeneous equation's solution possible the unknown integration multipler technique. Also, this simple technique's depend both sides of original homogeneous differential equation. The solution is slightly and more complicated if this integration into special form to be very complex. In this application's selected Ig=x^a.y^b integration multiplier technique for non-homogeneous form.
DIfactor( [ f1(x,y) , f2(x,y)] , flag )
f1(x,y) : Non-homogeneous differential equation's M(x,y) function
f2(x,y) : Non-homogeneous differential equation's N(x,y) function
flag : If flag=1 than solution be perceive application else small solution
General differential equation's
[M(x,y)]dx + [N(x,y)]dy = 0
[2*x^3*y^4 - 5*y]dx + [x^4*y^3 - 7*x]dy = 0
M(x,y)= f1(x,y) = [2*x^3*y^4 - 5*y]
N(x,y)= f2(x,y) = [x^4*y^3 - 7*x]
Matlab sub function application
DIfactor( [2*x^3*y^4 - 5*y , x^4*y^3 - 7*x] , 1) ;
Example1.pdf (Analytical solution)
DIfactor.m (sub function Matlab)
example.m (run sub function)
 Differential equations,PhD.Frank Ayres, Schaum's outline series and McGraw-Hill Company ,1998
 Mathematical handbook of formulas and tables,PhD. Murray R. Spiegel, PhD. John Liu, Second edition,McGraw-Hill book company,2001,ISBN:0-07-038203-4
 Differansiyel denklemler, Yrd.Do?.Dr. A.Ne?e Dernek, Do?.Dr.Ahmet,Dernek, Marmara university,Deniz book publisher,Istanbul,1995
Ali OZGUL (2023). First-Order Degree Linear Differential Equations (Integration factor Ig=x^a*y^b) (Update: 23-06-07) (https://www.mathworks.com/matlabcentral/fileexchange/15408-first-order-degree-linear-differential-equations-integration-factor-ig-x-a-y-b-update-23-06-07), MATLAB Central File Exchange. Retrieved .
MATLAB Release Compatibility
Platform CompatibilityWindows macOS Linux
Inspired by: Jean Le Rand D'Alambert Reduction Method (update:22-06-07)
Inspired: Regular solving technique as sub-function (update:24-07-07), Non-homogeneous and linear-differential-equation solutions (update:13-07-07)
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