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
Iteru [2.4K]
3 years ago
15

Use the substitution y equals x Superscript r to find a general solution to the given equation for x greater than 0. x cubed y t

riple prime (x )plus 3 x squared y double prime (x )minus 9 xy prime (x )minus 24 y (x )equals0

Mathematics
2 answers:
Anestetic [448]3 years ago
8 0

Answer:

The problem solution  is given in the attachments.

Georgia [21]3 years ago
4 0

Answer:

Step-by-step explanation:

Answer:

y = C1x^4 + (1/x²)[C2cos(√2)lnx + C3sin(√2)lnx]

Step-by-step explanation:

Given the differential equation

x³y'''(x) + 3x²y''(x) - 9xy'(x) - 24y(x) = 0 .........................................................(1)

We are required to solve the differential equation, using the substitution,

y = x^r

Differentiating this three times in succession, to obtain y', y'', and y'''. We have

y' = rx^(r - 1)

y'' = r(r - 1)x^(r - 2)

y''' = r(r - 1)(r - 2)x^(r - 3)

Using these in (1), we have

x³r(r - 1)(r - 2)x^(r - 3) + 3x²r(r - 1)x^(r - 2) - 9xrx^(r - 1) - 24x^r = 0

[r(r - 1)(r - 2) + 3r(r - 1) - 9r - 24]x^r = 0

But x^r ≠ 0

So

r(r - 1)(r - 2) + 3r(r - 1) - 9r - 24 = 0

r³ - 3r² + 2r + 3r² - 3r - 9r - 24 = 0

r³ - 10r - 24 = 0

(r - 4)(r² + 4r + 6) = 0

r - 4 = 0

r = 4 ..........................................(a)

r² + 4r + 6 = 0

Using the quadratic formula

r = [-b ± √(b² - 4ac)]/2a

Where a = 1, b = 4, and c = 6

r = [-4 ± √(16 - 24)]/2

= -4/2 ± (1/2)√(-8)

r = -2 ± i√2 ....................................(b)

From (a) and (b), we have

r = 4, -2 ± i√2

Since y = x^r

The solution is therefore

y = C1x^4 + (1/x²)[C2cos(√2)lnx + C3sin(√2)lnx]

You might be interested in
An 8-car Ferris wheel is shaped like a regular octagon. Does the Ferris wheel have rotational symmetry?
sleet_krkn [62]

Answer:

Yes, it does.

Step-by-step explanation:

Every regular shaped figure will have rotational symmetry, since they are built with identical segments all around.

To find the answer, ask yourself « If I rotate the shape, is there a time where I’ll find the exact same shape again with a different angle? »

So, a square has rotational symmetry, but not a rectangle.

A equilateral triangle has rotational symmetry, but not any other type of triangle.

8 0
3 years ago
Solve.<br> 4x -6= 14<br> X=?
levacccp [35]

Answer: x = 5

Step-by-step explanation: You Have To Move The Number 6 to the right beause it has no variable then solve the equation.

6 0
3 years ago
Read 2 more answers
11.5 is what percent of 8? Round to the nearest tenth.
Alik [6]

Answer:

143.8% is the answer

6 0
3 years ago
Read 2 more answers
Please help :) !!!!!!!!!!!
Mrrafil [7]
8. 70.5* 10. 30* 12. 5.1*
5 0
3 years ago
The interior of a safe is shaped like a cube with edges 9 inches long. What is the volume of the interior of the safe?
fgiga [73]

Answer:

Assuming that all three sides are 9 inches then the answer should 729.

Step-by-step explanation:

Just multiply 9*9*9. The formula to get volume is (length)*(width)*(height).

3 0
3 years ago
Other questions:
  • What is a root of a polynomial function?
    7·2 answers
  • Twelve boys collected 16 aluminum cans each. Fifteen girls collected 14 aluminum cans each. How many more cans did the girls col
    5·2 answers
  • For any positive integer n, the sum of the first n positive integers equals n(n+1)2n(n+1)2. what is the sum of all the even inte
    6·2 answers
  • 2.Mrs. Fernandez and Mrs.Bosiljevac invaded the biology lab! They find some bacterial cultures and decide to experiment. Mrs. Fe
    6·1 answer
  • Help!! Use #8-10 to answer #11
    6·1 answer
  • Need 9 asap pls it’s eary
    6·1 answer
  • Solve for h: 45 = h+ 19
    9·2 answers
  • PLZZZZZZZZZZZZ PLZZZZZZZZZZZZ PLZZZZZZZZZZZZ PLZZZZZZZZZZZZ help
    6·2 answers
  • Use any strategy to solve each problem.
    14·1 answer
  • Squaring the product of z and 5 gives the same
    5·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!