Linear Differential Equations in n th-order

بسم الله الرحمن الرحيم


Linear Differential Equations in n th-order ;

An nth-order linear differential equation has the form ;
? y?^((n))+a_(n-1 ) (x) ? y?^((n-1))+?+a_(2 ) (x) ? y?^ +a_(1 ) (x) ? y?^ +a_(0 ) (x)y=?(x) …. (1)
Where the coefficients a_(j ) (x) ;(j=0,1,2,…,n-1) ,and ?(x) depends solely on the variable x (not on y or any derivative of y)
If ?(x)=0 then Eq.(1) is homogenous ,if not then is nonhomogeneous .
? y?^((n))+a_(n-1 ) (x) ? y?^((n-1))+?+a_(2 ) (x) ? y?^ +a_(1 ) (x) ? y?^ +a_(0 ) (x)y=0 ……(2)
A linear differential equation has constant coefficients if all the coefficients a_(j ) (x) are constants ,if one or more is not constant then has variable coefficients














An nth-order linear differential equation has the form ;
? y?^((n))+a_(n-1 ) (x) ? y?^((n-1))+?+a_(2 ) (x) ? y?^ +a_(1 ) (x) ? y?^ +a_(0 ) (x)y=?(x) …. (1)
Where the coefficients a_(j ) (x) ;(j=0,1,2,…,n-1) ,and ?(x) depends solely on the variable x (not on y or any derivative of y)
If ?(x)=0 then Eq.(1) is homogenous ,if not then is nonhomogeneous .
? y?^((n))+a_(n-1 ) (x) ? y?^((n-1))+?+a_(2 ) (x) ? y?^ +a_(1 ) (x) ? y?^ +a_(0 ) (x)y=0 ……(2)
A linear differential equation has constant coefficients if all the coefficients a_(j ) (x) are constants ,if one or more is not constant then has variable coefficients











An nth-order linear differential equation has the form ;
? y?^((n))+a_(n-1 ) (x) ? y?^((n-1))+?+a_(2 ) (x) ? y?^ +a_(1 ) (x) ? y?^ +a_(0 ) (x)y=?(x) …. (1)
Where the coefficients a_(j ) (x) ;(j=0,1,2,…,n-1) ,and ?(x) depends solely on the variable x (not on y or any derivative of y)
If ?(x)=0 then Eq.(1) is homogenous ,if not then is nonhomogeneous .
? y?^((n))+a_(n-1 ) (x) ? y?^((n-1))+?+a_(2 ) (x) ? y?^ +a_(1 ) (x) ? y?^ +a_(0 ) (x)y=0 ……(2)
A linear differential equation has constant coefficients if all the coefficients a_(j ) (x) are constants ,if one or more is not constant then has variable coefficients