Solving of Nonhomogeneous Linear Differential Equations

بسم الله الرحمن الرحيم

Solving of Nonhomogeneous Linear Differential Equations


The nonhomogeneous diff. eq. with form second order ;
a_(2 ) (x) (d^2 y)/(dx^2 )+a_(1 ) (x) dy/dx+a_(0 ) (x)y=g(x) ….(1)
Where a_(2 ) (x)?0 and a_(1 ) (x) ? ,a?_(0 ) (x) and g(x) are continuous functions for x on an interval I .
To find the general solution for nonhomogeneous eq.(1) ,it is necessary to;
Find the general solution y_c of the associated homogeneous equation
a_(2 ) (x) (d^2 y)/(dx^2 )+a_(1 ) (x) dy/dx+a_(0 ) (x)y=0 ….(2)
as a complementary function
Add y_c to the particular solution y_p of eq.(1) .
Thus there are several methods to find y_p of eq.(1

The nonhomogeneous diff. eq. with form second order ;
a_(2 ) (x) (d^2 y)/(dx^2 )+a_(1 ) (x) dy/dx+a_(0 ) (x)y=g(x) ….(1)
Where a_(2 ) (x)?0 and a_(1 ) (x) ? ,a?_(0 ) (x) and g(x) are continuous functions for x on an interval I .
To find the general solution for nonhomogeneous eq.(1) ,it is necessary to;
Find the general solution y_c of the associated homogeneous equation
a_(2 ) (x) (d^2 y)/(dx^2 )+a_(1 ) (x) dy/dx+a_(0 ) (x)y=0 ….(2)
as a complementary function
Add y_c to the particular solution y_p of eq.(1) .
Thus there are several methods to find y_p of eq.(1
The nonhomogeneous diff. eq. with form second order ;
a_(2 ) (x) (d^2 y)/(dx^2 )+a_(1 ) (x) dy/dx+a_(0 ) (x)y=g(x) ….(1)
Where a_(2 ) (x)?0 and a_(1 ) (x) ? ,a?_(0 ) (x) and g(x) are continuous functions for x on an interval I .
To find the general solution for nonhomogeneous eq.(1) ,it is necessary to;
Find the general solution y_c of the associated homogeneous equation
a_(2 ) (x) (d^2 y)/(dx^2 )+a_(1 ) (x) dy/dx+a_(0 ) (x)y=0 ….(2)
as a complementary function
Add y_c to the particular solution y_p of eq.(1) .
Thus there are several methods to find y_p of eq.(1