Find the general solutions of the differential equations 6y^{4} +11y"+4y

hadejada7x 2021-12-27 Answered
Find the general solutions of the differential equations 6y4+11y4y=0
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Mary Nicholson
Answered 2021-12-28 Author has 38 answers
6y4+11y4y=0 (1)
Eq (1) can be written as
(6D4+11D2+4)y=0
AE. 6m4+11m2+4=0
For value of m we put m2=u
m4=42
6u2+11u+4=0
u=12 u=43
m2=12 m2=43
m=±i12 m=±i43=±i233=±i23
Which is comple roots.
y=c1cos(12t)+c2sin(12t)+c3cos(2t3)+c4sin(2t3)
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Mary Nicholson
Answered 2021-12-29 Author has 38 answers
The auxilary equation is,
6m4+11m2+4=0
m2=11±1219612=12,43
m=±i2,±2i3
If α±iβ are the roots of auxilary equation, then the solution is y=eαx(c1cosβx+c2sinβx)
Thus, the required solution is,
y=(c1cosx2+c2sinx2)+(c3cos2x3+c4sin2x3)
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karton
Answered 2022-01-10 Author has 439 answers

m=6±624(1)(11)2(1)=6±82=6±i82=6±2i22=3±i2y=e3x(C1sin2x+C2cos2x)

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