#4y''+36y="cosec"(3x)#, can u please help me to solve this equation?
this is a problem of variation of parameter
this is a problem of variation of parameter
2 Answers
See below.
Explanation:
This is a linear non-homogeneous differential equation. Those DE heve a solution that can be composed as
The solution for
(see my answer to https://socratic.org/questions/y-9y-0-y1-sin3x-by-using-reduction-of-order-method-how-can-i-solve-this-equation )
Now the particular solution for
is
and finally
Explanation:
Characteristic equation of this differential one:
Its roots are
Consequently homogeneous solution of it is:
I used variation of parameters for finding particular solution
In this case
According to this method,
From first equation,
Hence,
Consequently,
Thus,