First-Order Degree Linear Differential Equations (Integration factor Ig=x^a*y^b) (Update: 23-06-07)

Homogeneous or non-homogeneous linear dif. eq.

[DESCRIPTION]

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.

[SYNTAX]

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

[EXAMPLE]

[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) ;

[ZIP ARCHIVE]
Example1.pdf (Analytical solution)
Example2.pdf
Example3.pdf
DIfactor.m (sub function Matlab)
example.m (run sub function)
example.html

[REFERENCES]

[1] Differential equations,PhD.Frank Ayres, Schaum's outline series and McGraw-Hill Company ,1998

[2] 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

[3] Differansiyel denklemler, Yrd.Do?.Dr. A.Ne?e Dernek, Do?.Dr.Ahmet,Dernek, Marmara university,Deniz book publisher,Istanbul,1995