Solve the following differential Equation

gorovogpg 2021-12-26 Answered
Solve the following differential Equation
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esfloravaou
Answered 2021-12-27 Author has 43 answers
Joseph Fair
Answered 2021-12-28 Author has 34 answers
D4y8D3y+24D2y32Dy+16y=0
(D48D3+24D232D+16)y=0
Auxiliary Equation
m48m3+24m232m+16=0
Let m=2,f(2)=248(2)3+24(2)232(2)+16
=1664+9664+16
=128128=0
m26m2+12m8=0
(m2)3=0
(m2)3=0(m2)(m2)(m2)
m=2,2,2,2 are the four repeated roots
The solution is of the form
yc(t)=(C1+C2t+C3t2+C4t3)emt
=(C1+C2t+C3t2+C4t3)e2t
Result: we obtain real and equal roots with multiplicity 4
y(t)=(C1+C2t+C3t2+C4t3)e2t
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karton
Answered 2022-01-09 Author has 439 answers

D4y8D3y+24D2y32Dy+16y=0(D48D3+24D232D+16)y=0m48m3+24m232m+16=0m=2,f(2)=248(2)3+24(2)232(2)+16=1664+9664+16=128128=0m26m2+12m8=0(m2)3=0(m2)3=0(m2)(m2)(m2)m=2,2,2,2yc(t)=(C1+C2t+C3t2+C4t3)emt=(C1+C2t+C3t2+C4t3)e2ty(t)=(C1+C2t+C3t2+C4t3)e2t

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