1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
crimeas [40]
3 years ago
6

Find a homogeneous linear differential equation with constant coefficients whose general solution is given by

Mathematics
1 answer:
frez [133]3 years ago
6 0

Answer:

y" + 2y' + 2y = 0

Step-by-step explanation:

Given

y=c_1e^{-x}cosx+c_2e^{-x}sinx

Required

Determine a homogeneous linear differential equation

Rewrite the expression as:

y=c_1e^{\alpha x}cos(\beta x)+c_2e^{\alpha x}sin(\beta x)

Where

\alpha = -1 and \beta = 1

For a homogeneous linear differential equation, the repeated value m is given as:

m = \alpha \± \beta i

Substitute values for \alpha and \beta

m = -1 \± 1*i

m = -1 \± i

Add 1 to both sides

m +1= 1 -1 \± i

m +1= \± i

Square both sides

(m +1)^2= (\± i)^2

m^2 + m + m + 1 = i^2

m^2 + 2m + 1 = i^2

In complex numbers:

i^2 = -1

So, the expression becomes:

m^2 + 2m + 1 = -1

Add 1 to both sides

m^2 + 2m + 1 +1= -1+1

m^2 + 2m + 2= 0

This corresponds to the homogeneous linear differential equation

y" + 2y' + 2y = 0

You might be interested in
Which arc is a minor arc?
Nadusha1986 [10]

A minor arc is an arc of a circle having measure less than or equal to radians and it is an arc smaller than a semicircle. In the given figure, EC is the minor arc as it is an arc smaller than a semicircle. EGF, ECG and GCE are not the minor arcs as these arcs does not have measure less than or equal to radians and these arcs are also not smaller than a semicircle.

4 0
3 years ago
What helps in determining the reliability of a person wit reguard?
Nezavi [6.7K]
<span>credit score

</span>because the way and the time they pay the bill and taxes and it would be the same with debt <span>

Hope this helped!

:)</span>
6 0
3 years ago
Plsss help me ( I put a picture up )
Minchanka [31]
I'm pretty sure the 3rd one is right, use a calculator
3 0
3 years ago
Read 2 more answers
Someone want to help me with some Geometry?
Aleks04 [339]
The second answer that uses = is not correct, because the pentagons are similar not congruent.
The third answer is not correct, because that sign means estimated, not similar.
I've never seen the fourth sign, so by process of elimination I believe the answer is the first one.

<span>ABCDE~QRSTU</span>
8 0
3 years ago
P;EASE HELP!!!!!  Consider the leading term of the polynomial function. What is the end behavior of the graph? Describe the end
Marrrta [24]
<span>The end behavior of a polynomial function is the behavior of the graph of f as 
x → +∞ or x → -∞ , depending on its leading coefficient.

In the example, the LEADING COEFFICIENT = - 3x</span>⁵
<span>,when x → +∞, ( - 3x⁵ ) → - ∞ . The end behavior, the polynomial approches minus infinity



</span>
7 0
3 years ago
Other questions:
  • 2a , b and c with work please
    15·1 answer
  • What two numbers multiply to -52 and add up to -24
    7·1 answer
  • How long is a guy wire reaching from the top of a 6ft. Pole to a point on the ground 4ft. From the pole
    11·1 answer
  • (36xa - 30xb) ÷ (-6x2)
    11·1 answer
  • Which is the final line of her partial product and the correct answer? A. 0 . 4 × 2 = 0 . 8 ; 9.6 B. 0 . 4 × 0 . 2 = 0 . 08 ; 8.
    7·1 answer
  • Andy bought the Playstation 5 bundle on Black Friday for $399. The sales tax is 8.5%. What is the
    13·2 answers
  • Find the length of the hypotenuse.
    7·2 answers
  • Julie drank 4 5 liter of water Monday before going jogging. She drank 2 3 liter of water after her jog. How much water did Julie
    15·1 answer
  • Evaluate -8 × |2|.<br><br> A)-10<br> B)10<br> C)-16<br> D)16
    7·2 answers
  • Bath and Body Works is having a special promotion on fall candles. Every 12th guest is receiving a free pumpkin scented candle a
    6·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!