Particular Solution for Nonhomogeneous Differential Equations –Operator D Method

بسم الله الرحمن الرحيم

Particular Solution for Nonhomogeneous Differential Equations –Operator D Method


The nonhomogeneous diff. eq. with form by operator D ;
f(D)y=f(x)
So the particular solution for this eq. ;
y_p=(f(x))/(f(D))
Where
f(D)=D^2+a_(1 ) D+a_(0 )
Or P(D)y=(D^2+a_(1 ) D+a_(0 ) )y
















The nonhomogeneous diff. eq. with form by operator D ;
f(D)y=f(x)
So the particular solution for this eq. ;
y_p=(f(x))/(f(D))
Where
f(D)=D^2+a_(1 ) D+a_(0 )
Or P(D)y=(D^2+a_(1 ) D+a_(0 ) )y

















The nonhomogeneous diff. eq. with form by operator D ;
f(D)y=f(x)
So the particular solution for this eq. ;
y_p=(f(x))/(f(D))
Where
f(D)=D^2+a_(1 ) D+a_(0 )
Or P(D)y=(D^2+a_(1 ) D+a_(0 ) )y