Find a particular solution to y''-4y'+4y=(14e^{2t})/(t^2+1)

Meldeaktezl

Meldeaktezl

Answered question

2022-09-03

Find a particular solution to
y 4 y + 4 y = 14 e 3 t t 2 + 1

Answer & Explanation

Ufumanaxi

Ufumanaxi

Beginner2022-09-04Added 5 answers

The given differential equation is
y 4 y + 4 y = 14 e 2 t t 2 + 1
The particular solution is
y p = 1 D 2 4 D + 4 ( 14 e 2 t t 2 + 1 ) where D = d d x
= 1 ( D 2 ) 2 ( 14 e 2 t t 2 + 1 ) = 14 e 2 t 1 ( D + 2 2 ) 2 1 t 2 + 1 = 14 e 2 t 1 D 2 1 t 2 + 1 = 14 e 2 t 1 D tan 1 ( t ) = 14 e 2 t [ t tan 1 ( t ) t 1 + t 2 d t ] y p = 14 e 2 t [ t tan 1 1 2 log ( 1 + t 2 ) ]

Do you have a similar question?

Recalculate according to your conditions!

Ask your question.
Get an expert answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?