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
Masja [62]
3 years ago
14

y = c1 cos(5x) + c2 sin(5x) is a two-parameter family of solutions of the second-order DE y'' + 25y = 0. If possible, find a sol

ution of the differential equation that satisfies the given side conditions. The conditions specified at two different points are called boundary conditions. (If not possible, enter IMPOSSIBLE.) y(0) = 1, y'(π) = 9
Mathematics
1 answer:
TEA [102]3 years ago
3 0

Answer:

y = 2cos5x-9/5sin5x

Step-by-step explanation:

Given the solution to the differential equation y'' + 25y = 0 to be

y = c1 cos(5x) + c2 sin(5x). In order to find the solution to the differential equation given the boundary conditions y(0) = 1, y'(π) = 9, we need to first get the constant c1 and c2 and substitute the values back into the original solution.

According to the boundary condition y(0) = 2, it means when x = 0, y = 2

On substituting;

2 = c1cos(5(0)) + c2sin(5(0))

2 = c1cos0+c2sin0

2 = c1 + 0

c1 = 2

Substituting the other boundary condition y'(π) = 9, to do that we need to first get the first differential of y(x) i.e y'(x). Given

y(x) = c1cos5x + c2sin5x

y'(x) = -5c1sin5x + 5c2cos5x

If y'(π) = 9, this means when x = π, y'(x) = 9

On substituting;

9 = -5c1sin5π + 5c2cos5π

9 = -5c1(0) + 5c2(-1)

9 = 0-5c2

-5c2 = 9

c2 = -9/5

Substituting c1 = 2 and c2 = -9/5 into the solution to the general differential equation

y = c1 cos(5x) + c2 sin(5x) will give

y = 2cos5x-9/5sin5x

The final expression gives the required solution to the differential equation.

You might be interested in
Can you help me plz
Alex73 [517]

9514 1404 393

Answer:

  y = x + 4

Step-by-step explanation:

To find the constant in the equation, look in the table for the value of y when x=0. That value is 4, so ...

  y = x + 4

6 0
3 years ago
There is a circle with a center of 0,0 on a coordinate plane. There is one point on the circle's circumference in which the x:y
abruzzese [7]

Answer:

Step-by-step explanation:

Suppose the radius is 1. The parametric equations for the circle are

x = cosθ

y = sinθ

x:y = 3:1

tanθ = ⅓

cosθ = 3/√(1²+3²) =  3/√10

sinθ = 1/√10

The solutions are (3/√10, 1/√10) and (-3/√10, -1/√10).

6 0
3 years ago
Which transformation is a translation?
astra-53 [7]

Answer:

[2] Translation

[4]Transformation

Step-by-step explanation:

Translation is just moving the shape.

Transformation is changing the shape and tilting it changed the shape.

7 0
3 years ago
An open box is formed from a rectangular piece of cardboard whose length is 8cm more than its width by cutting squares of 2cm fr
Serggg [28]
If the width of the cardboard = x cm then its length is given by x + 8 cm.
Then the length of the box will be x + 8 - 2(2) =  x + 4
and the width = x - 2(2) = x - 4 cm The height is 2 cm 

Volume = h*w*l = 2(x - 4)(x + 4) = 256
2(x^2 - 16) = 256
x^2 - 16 = 128
x^2  = 144 
x = 12 cm 

Dimensions of the box are:-

length =  12 + 4 =  16cm
width = 12 - 4 = 8 cm
height = 2 cm



















3 0
3 years ago
Select all of the potential solution(s) of the equation 2log5x = log54.
tankabanditka [31]

Answer:

-2 and 2

Step-by-step explanation: just did the problem

4 0
3 years ago
Other questions:
  • Expressions that have the same value
    15·1 answer
  • What is the missing angel in the triangle 69,34,
    14·2 answers
  • What is the answer here please. Brainliest to those who answer
    6·1 answer
  • What is 84/144 in simplest form fraction?
    15·1 answer
  • Please can someone help quick and now 115 students choose to attend one of three after school activities: football, tennis or ru
    13·1 answer
  • F(x)=x^2. what is g(x)?
    10·1 answer
  • Carlos has $24, which is 1 1/3 as much money as Luisa has. How much money does Luisa have?
    14·2 answers
  • PLEASE HELPPPPP!!!!!
    12·1 answer
  • Which of the following exponential equations is equivalent to the logarithmic
    8·2 answers
  • 4. Which of the following can be used
    11·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!