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
alekssr [168]
2 years ago
9

Verify that the indicated family of functions is a solution of the given differential equation. Assume an appropriate interval I

of definition for each solution.
d^2y/ dx^2 − 6 dy/dx + 9y = 0; y = c1e3x + c2xe3x When y = c1e3x + c2xe3x,
Mathematics
1 answer:
Rufina [12.5K]2 years ago
3 0

<em>y''</em> - 6<em>y'</em> + 9<em>y</em> = 0

If <em>y</em> = <em>C₁ </em>exp(3<em>x</em>) + <em>C₂</em> <em>x</em> exp(3<em>x</em>), then

<em>y'</em> = 3<em>C₁ </em>exp(3<em>x</em>) + <em>C₂</em> (exp(3<em>x</em>) + 3<em>x</em> exp(3<em>x</em>))

<em>y''</em> = 9<em>C₁ </em>exp(3<em>x</em>) + <em>C₂</em> (6 exp(3<em>x</em>) + 9<em>x</em> exp(3<em>x</em>))

Substituting these into the DE gives

(9<em>C₁ </em>exp(3<em>x</em>) + <em>C₂</em> (6 exp(3<em>x</em>) + 9<em>x</em> exp(3<em>x</em>)))

… … … - 6 (3<em>C₁ </em>exp(3<em>x</em>) + <em>C₂</em> (exp(3<em>x</em>) + 3<em>x</em> exp(3<em>x</em>)))

… … … + 9 (<em>C₁ </em>exp(3<em>x</em>) + <em>C₂</em> <em>x</em> exp(3<em>x</em>))

= 9<em>C₁ </em>exp(3<em>x</em>) + 6<em>C₂ </em>exp(3<em>x</em>) + 9<em>C₂ x</em> exp(3<em>x</em>))

… … … - 18<em>C₁ </em>exp(3<em>x</em>) - 6<em>C₂</em> (exp(3<em>x</em>) - 18<em>x</em> exp(3<em>x</em>))

… … … + 9<em>C₁ </em>exp(3<em>x</em>) + 9<em>C₂</em> <em>x</em> exp(3<em>x</em>)

= 0

so the provided solution does satisfy the DE.

You might be interested in
What is the domain and range​
kogti [31]

Answer:

The domain is all the x-values, and the range is all the y-values

Step-by-step explanation:

7 0
3 years ago
Which of these numbers is divisible by 8,,, 7116 4309 ,,,4136,,, 9406
Nikolay [14]


4136/8= 517

The others
7116/8=889.5
4309/8=538.625
9406/8=1175.75
4 0
3 years ago
Read 2 more answers
Which of the following is the estimated amount of salt that will dissolve at 47 degrees?
Nina [5.8K]

Ths solubility curve can be used to obtain the amount of salt dissolved (solubility).

<h3>What is the solubility curve?</h3>

The solubility curve is a plot of the solubility of a substance against the temperature. It serves the purpose of being used to show the solubility of a susbtance at different temperatures. This question is incomplete hence we can not be able to deduce the solubility of the salt at this temperature.

If the solubility curve has been ploted, then we can be able to estimate the solubility of the salt from the graph.

Learn more about solubility curve: brainly.com/question/9537462

8 0
2 years ago
One sprinter has a stride of 120cm, another 75cm. How many steps do they each take if they run a 100m race?
Olenka [21]

Answer:

1m = 100 cm

First sprinter stride is 120 cm. Steps he will take

= 100/1.2 = 83 1/3 steps

Second sprinter takes a stride of 75 cm

= 100/0.75 = 133 1/3 steps

3 0
3 years ago
The magnitude of an earthquake is calculated using the Richter Scale, M=log I/io , where I0 is the threshold intensity and the i
marysya [2.9K]

Answer:

The answer is <u><em>log(980)! :)</em></u>

5 0
3 years ago
Other questions:
  • How to rewright 16^3/4
    8·2 answers
  • Circle the number which is nearest in value to 750570 699 810 852 1050
    7·1 answer
  • Jessica want to slowly decrease her daily caloric intake, which is currently 2500 calories per day. She plans to decrease her ca
    15·1 answer
  • What times what equals 11, but if you add the numbers together you get 12.
    13·2 answers
  • A middle school took all of its 6th grade students on a field trip to see a play. The students filled 2200 seats, which was 55%
    6·2 answers
  • Can someone pls tell me this answer which I have shown in the screenshot pls
    12·1 answer
  • What is the minimum y-value after which the exponential function will always be greater than the linear function? y = 1 y = 3 y
    11·1 answer
  • 5.93x0.85 slove the answer for me
    6·2 answers
  • Ariana is shipping 8 bags of granola to a customer. Each bag weighs 22 ounces and the maximum weight she can ship in one box is
    14·1 answer
  • Jules is measuring a patient’s height at 4 feet What is this height in inches? Answer
    5·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!