Method of Solving Homogeneous Equations with Variable Coefficients

بسم الله الرحمن الرحيم

Method of Solving Homogeneous Equations with Variable Coefficients;
The homogeneous diff. eq. with form second order ;
a_(2 ) (x) y^ +a_(1 ) (x)y^ +a_0 (x)y=0 ….(1)
Where the coefficients a_(j ) (x) ;(j=0,1,2) are functions for x ,can be written as;
y +(a_(1 ) (x))/(a_(2 ) (x) ) y^ +(a_0 (x))/(a_(2 ) (x) ) y=0
Where a_(2 ) (x)?0 for all x in the interval I .
Thus y +p(x)y^ +q(x)y=0 ….(2)
Where the functions p(x)=(a_(1 ) (x))/(a_(2 ) (x) ) , q(x)=(a_0 (x))/(a_(2 ) (x) ) are continuous of x in the interval










The homogeneous diff. eq. with form second order ;
a_(2 ) (x) y^ +a_(1 ) (x)y^ +a_0 (x)y=0 ….(1)
Where the coefficients a_(j ) (x) ;(j=0,1,2) are functions for x ,can be written as;
y +(a_(1 ) (x))/(a_(2 ) (x) ) y^ +(a_0 (x))/(a_(2 ) (x) ) y=0
Where a_(2 ) (x)?0 for all x in the interval I .
Thus y +p(x)y^ +q(x)y=0 ….(2)
Where the functions p(x)=(a_(1 ) (x))/(a_(2 ) (x) ) , q(x)=(a_0 (x))/(a_(2 ) (x) ) are continuous of x in the interval











The homogeneous diff. eq. with form second order ;
a_(2 ) (x) y^ +a_(1 ) (x)y^ +a_0 (x)y=0 ….(1)
Where the coefficients a_(j ) (x) ;(j=0,1,2) are functions for x ,can be written as;
y +(a_(1 ) (x))/(a_(2 ) (x) ) y^ +(a_0 (x))/(a_(2 ) (x) ) y=0
Where a_(2 ) (x)?0 for all x in the interval I .
Thus y +p(x)y^ +q(x)y=0 ….(2)
Where the functions p(x)=(a_(1 ) (x))/(a_(2 ) (x) ) , q(x)=(a_0 (x))/(a_(2 ) (x) ) are continuous of x in the interval