The general solution to the second-order differential equation 9y''+12y'+4y=0 is

FizeauV

FizeauV

Answered question

2021-09-27

The general solution to the second-order differential equation 9y+12y+4y=0 is in the form y(x)=c1erx+c2xerx. Find the value of r.
Answer: r=?

Answer & Explanation

tabuordy

tabuordy

Skilled2021-09-28Added 90 answers

Step 1
Create the auxiliary equation that goes with it:
9r2+12r+4=0
9r2+6r+6r+4=0
3r(3r+2)+2(3r+2)=0
(3r+2)(3r+2)=0
(3r+2)2=0r=23
Step 2
Therefore, the given differential equation's solution is y(x)=c1erx+c2xerx where r=23

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