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
Rashid [163]
3 years ago
8

Determine for which values of m the function variant Φ(x) = x^m is a solution to the given equation. a. 3x^2 (d^2y/dx^2) + 11x(d

y/dx) - 3y = 0 b. x^2 (d^2y/dx^2) - x(dy/dx) - 5y = 0

Mathematics
2 answers:
miv72 [106K]3 years ago
7 0

Answer:

a)  m = -9 or m = 1

b) m =  1 + √6 or m = 1 -√6

Step-by-step explanation:

for

Φ(x) = x^m

then

dΦ/dx (x) = m*x^(m-1)

d²Φ/dx² (x) = m*(m-1)*x^(m-2)

then

for a

3x^2 (d^2y/dx^2) + 11x(dy/dx) - 3y = 0

3x^2*m*(m-1)*x^(m-2) + 11*x* m*x^(m-1) - 3*x^m = 0

3*m*(m-1)*x^m + 11*m*x^m- 3*x^m = 0

dividing by x^m

3*m*(m-1) + 11*m - 3 =0

3*m² + 8 m - 3 =0

m= [-8 ± √(64 + 4*3*3)]/2 = (-8±10)/2  

m₁ = -9 , m₂= 1

then Φ(x) = x^m is a solution for the equation a , when m = -9 or m = 1

for b)

x^2 (d^2y/dx^2) - x(dy/dx) - 5y = 0

x^2*m*(m-1)*x^(m-2) -  x* m*x^(m-1) - 5*x^m = 0

m*(m-1)*x^m -m *x^m- 5*x^m = 0

dividing by x^m

m*(m-1) -m - 5 =0

m² - 2 m - 5 =0

m= [2 ± √(4 + 4*1*5)]/2 = (2±√24)/2 = 1 ±√6

m₁ =  1 + √6 , m₂ =  1 - √6

then Φ(x) = x^m is a solution for the equation b , when m =  1 + √6 or m = 1 - √6

zubka84 [21]3 years ago
6 0

Answer

a) m = -3 or 1/3

b) m = 1 + root 6 or 1 - root 6

Step-by-step explanation:

The step by step calculation is as shown in the attachment.

You might be interested in
You and your brother are reading the same novel. You want to get ahead of him in the book, so you decide to read 30 minutes long
Sholpan [36]

Answer: its 45 if i read it right.

Step-by-step explanation:

8 0
3 years ago
Can someone please solve 7???
cestrela7 [59]

Answer:

A

Step-by-step explanation:

Sum the parts of the ratio, 5 + 3 = 8 parts

Divide the total area by 8 to find the value of one part of the ratio.

1624 ÷ 8 = 203 cm² ← value of 1 part of ratio, thus

Area of B = 3 × 203 = 609 cm² → A

3 0
3 years ago
Read 2 more answers
Is 6 less than 6.00?
Nadya [2.5K]
No, they are the same value.
3 0
3 years ago
1. Solve for the variable. x - 4.5 = 11.3 ​
polet [3.4K]

Answer:

15.8

Step-by-step explanation:

do 11.3 + 4.5 = 15.8

7 0
3 years ago
Read 2 more answers
What is the slope of a line perpendicular to the line whose equation is 4x+5y=354x+5y=35. Fully simplify your answer.
IrinaK [193]

The perpendicular slope is expressed as the negative reciprocal of the slope or − 1 m. In this scenario, the slope, or m, is −4 so the slope of the perpendicular line is − 1 −4 which simplifies to 1 4

5 0
1 year ago
Other questions:
  • Which year had an upward trend between month 3 and month 4? this year or last year?
    9·1 answer
  • kamal has 2 liters of soup. he pours it into 4 bowls each bowl gets an equal amount how many milliliters of soup are in each bow
    14·2 answers
  • A. 5pi/6<br> B. 8pi/6<br> C. 3pi/6<br> D. 13pi/6
    10·1 answer
  • There are 30.38 centimeters in 1 foot. Which speed equals 50 ft/min?
    11·1 answer
  • Consider the geometric sequence 1/64, 1/16, 1/4, 1, …. What is the common ratio?
    7·2 answers
  • What is a Corresponding angle?
    5·2 answers
  • Write 1/5 as a percent.
    12·2 answers
  • 1. What is the constant rate of change of the table below?
    11·1 answer
  • Hello, I really wants some steps that are simple to solve this problem. I need to find
    15·2 answers
  • What binomial do you have to add to the polynomial 2x^2+3y^2-5xy+1 to get the following?
    6·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!