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
HELP I NEED THIS SOLVED IN SIMPLEST FORM!!<br> 5/6 + 1/2 =
sammy [17]

Answer:

8/6 or  1 1/3

Step-by-step explanation:

to add 5/6 and 1/2 you have to find the LCD for both fractions

This would be 6.

So 5/6 would remain the same and 1/2 would become 3/6 because 2*3 = 6 and 1*3=3.

Then you would add them, but keep the denominator and get 8/6 an improper fraction.

If you have to simplify further, then it would be the mixed number 1 2/6, which when simplified further is 1 1/3.

As a decimal it is 1.33333333333333333333333333333333

7 0
3 years ago
Read 2 more answers
pablos pizza shop made a profit of $495 each day for 12 days. what is the total profit for all 12 days
a_sh-v [17]

Answer:

$5940

Step-by-step explanation:

multiply 495 x 12 = 5940

Pablos pizza gain a profit of $5940 in 12 days.

4 0
2 years ago
I need help with this... 4 more than some number d. and 3 is less than X. and the others :(
Greeley [361]
2) C: 4+d

3) A: x-3

4) C: 5(1-f)

I know that this is a few weeks late...

but hope this helps!
3 0
3 years ago
Help asap please!!!!
Novay_Z [31]
(4,-3) I believe- I got it bc x1 is 3 away from x2 and same with y1 and y2
5 0
3 years ago
1 US Dollar =13.05 pesos 1meter =1.094 yars
Evgesh-ka [11]

Answer:

$18.01

Step-by-step explanation:

Convert from pesos to US dollars

6429/13.05 = $492.64

Convert from meters to yards

1.904* 25= 27.35

Divide to find the cost of one yard of fabric

492.64/27.35 = $18.01

4 0
3 years ago
Other questions:
  • At Silver Gym, membership is $45 per month, and personal training sessions are $35 each.
    10·1 answer
  • The dimension of a rectangular prism are 5cm, 5 cm, and 2 cm determine the surface area
    10·1 answer
  • What number would go in the blank? 4 x 6 = 6 x ___<br> 6<br><br> 4<br><br> 10
    13·1 answer
  • Solve the triangle given that a=19 b=16, c=11.
    11·1 answer
  • X and y intercept please :)
    10·2 answers
  • these are the cost and revenue functions for a product line of cat food sold in 70 lb bags at a single pet store based on the fu
    9·1 answer
  • 1.) Phoebe has a hunch that older students at her high school are more likely to bring
    5·1 answer
  • Rearrange each of the following in slope/y-intercept form, y = mx + b.
    8·2 answers
  • 3.0
    10·1 answer
  • Please help<br><br><br><br> ?? <br><br><br><br><br><br> :$):’jfidifkvk
    10·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!