# stuck in basic math of general method for differential equations

#### sabishaw

##### New member
hi there.....
I was just reviewing my class notes and i just cant understand how i solved my problems via general method.....i know and understand this method very well, but i just have missed something,that i cane even understand my own notes for a couple of alike problems.....
problem: (D^2 + a^2)y = sec(aX)
to be solved via general method of differential equations..
now there comes somewhere
P.I=sec(aX)/(D^2+a^2)
= sec(aX)/(D-ia)(D+ia) <<<<--------------------- what is this??
{i =iota}
or if anyone knows anyother way to solve it by general method,...please do help

#### tkhunny

##### Moderator
Staff member
D^2 + a^2 = 0 is a Characteristic (or auxiliary or Polynomial) equation which, upon solving, gives the General Solution of the Differential Equation.

• topsquark

#### sabishaw

##### New member
what is D-ia,....where did ia come from.....
thanks

#### tkhunny

##### Moderator
Staff member
What do you get when you factor the characteristic equation over Complex Numbers?

D=+ai,-ai