Solve the for the general solution of the differential equation (D^{6}+6D^{4}+12D^{2}+8)y=0

cistG

cistG

Answered question

2021-05-12

Solve the for the general solution of the differential equation
(D6+6D4+12D2+8)y=0

Answer & Explanation

smallq9

smallq9

Skilled2021-05-14Added 106 answers

Step 1
Given differential equation is
(D6+6D4+12D2+8)y=0 where D=ddx
Auxiliary equation is m6+6m4+12m2+8=0
Step 2
(m2+2)3=0   ((a+b)3=a3+3a2b+3ab2+b3)
m2=2,2,2
m=±2i,±2i,±2i
y=(c1x2+c2x+c3)cos(2x)+(c4x2+c5x+c6)sin(2x)

Jeffrey Jordon

Jeffrey Jordon

Expert2021-11-19Added 2605 answers

Answer is given below (on video)

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