(D^{3} - 14D + 8) y = 0

Zerrilloh6 2021-12-16 Answered
(D314D+8)y=0
You can still ask an expert for help

Want to know more about Laplace transform?

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more

Solve your problem for the price of one coffee

  • Available 24/7
  • Math expert for every subject
  • Pay only if we can solve it
Ask Question

Expert Answer

Cleveland Walters
Answered 2021-12-17 Author has 40 answers
Step 1. Differential equation
Homogeneous DE with constant coefficient- auxiliary equations:
(D314D+8)y=0
Differential equation:
In mathematics, a differential equation is an equation that relates one or more functions and their derivatives. In applications, the functions generally represent physical quantities, the derivatives represent their rates of change, and the differential equation defines a relationship between the two. Such relations are common; therefore, differential equations play a prominent role in many disciplines including engineering, physics, economics, and biology.
Step 2. Solution
D=m
m314m+8=0
m=4 is a factor,
m3+4m24m216m+2m+8=0
m2(n+4)4m(m+4)+2(m+4)=0
(m+4)(m24m+2)=0
m=4,
m=4±1682
m=4±222
m=2±2
Step 3. Solution
The complementary function is:
yc=c1e4x+e2x(c2cos2x+c3sin2x)
c1,c2,c3 are arbitrary constant.
Not exactly what you’re looking for?
Ask My Question
Mason Hall
Answered 2021-12-18 Author has 36 answers
Given that,
(D214D+8)y=0
The auxilary equation of above eq-n is-
m314m+8=0
m3+4m4m216m+2m+g=0
m2(m+4)4m(m+4)+2(m+4)=0
(m+4)(m24m=2)=0
(m+4)(m24m+2)=0
m+4=0 or m24m+2=0
m=4 or m=3.414,m=0.586
so, the roots of auxilary eq-n are real and distinct
Not exactly what you’re looking for?
Ask My Question
RizerMix
Answered 2021-12-29 Author has 438 answers

d=4
d=482=22=0.586
d=4+82=2+2=3.414
y=0

Not exactly what you’re looking for?
Ask My Question

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more