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
Inessa [10]
3 years ago
9

A homogeneous second-order linear differential equation, two functions y1 and y2 , and a pair of initial conditions are given be

low. First verify that y1 and y2 are solutions of the differential equation. Then find a particular solution of the form
y = c1y1 + c2y2 that satisfies the given initial conditions.
y'' + 49y = 0; y1 = cos(7x) y2 = sin(7x); y(0) = 10 y(0)=-4
y(x)=?
Mathematics
1 answer:
Basile [38]3 years ago
4 0

Answer:

Step-by-step explanation:

Check part

y= C_1y_1 + C_2y_2 = C_1cos(7x)+C_2sin(7x)

y'= -7 C_1sin(7x)+7C_2cos(7x)

y"= -49 C_1cos(7x) - 49 C_2sin(7x)

Now, replace to the original one.

y"+49 y = -49C_1cos(7x)-49 C_2 sin(7x) + 49 C_1cos(7x) +49 C_2sin(7x) = 0\\

Done!!

Particular solution

y(0) = C_1cos(0) + C_2 sin(0) = C_1= 10

I believe that y'(0) = 4, not y(0) anymore. Since y(0) CANNOT have two different solution.

y(0)'= -7 C_1sin(0) + 7 C_2 cos (0) = 7 C_2= -4

C_2 = -4/7

The last step is to put C1, C2 into your solution. You finish it.

You might be interested in
Solve the equation.<br><br> q+59=16<br> Thx!
e-lub [12.9K]

Answer:q= -43

Step-by-step explanation:

4 0
2 years ago
Read 2 more answers
The pairs 3, 12 and 4, 9 are factor pairs of which number? A) 32 B) 36 C) 44 D) 82
KatRina [158]

Answer:

\Huge \boxed{\mathrm{B) \ 36}}

\rule[225]{225}{2}

Step-by-step explanation:

A pair of factors are two factors of a number, when multiplied, gives the number.

3* 12=36

4*9=36

The pairs 3, 12 and 4, 9 are factor pairs of 36.

\rule[225]{225}{2}

6 0
3 years ago
Read 2 more answers
What is the solution to the system of two equations shown?
Nadya [2.5K]

The solution of the given system of equation is x = -3 and y = 4 respectively.      

<h3>What is a system of linear equations?</h3>

A system of linear equations can be defined as a number of equations needed to solve the equations. For n number of variables n number of equations are required.

The given system of equations is as,

y = 4x + 16                   (1)

y = −2x − 2                  (2)

In order to solve them, substitute equation (2) into (1) as follows,

4x + 16 = −2x − 2

=> 4x + 2x = -2 - 16

=> 6x = -18

=> x  = -3

Then, y = -2 × -3 - 2 = 4

Hence, the solution of the given system of equation is x = -3 and y = 4.  

To know more about system of equations click on,

brainly.com/question/24065247

#SPJ1    

6 0
8 months ago
This is what i need help on
Scilla [17]
G2=g1*2
g3=g1*2²
196=x*4
/4        /4
49
7 0
3 years ago
Translate each phrase into a variable expression. use n for the variable
gayaneshka [121]
N + 2 that is correct
8 0
3 years ago
Read 2 more answers
Other questions:
  • Mr. Stevens is 63 years older than his grandson, Tom. In 3 years Mr. Stevens will be four times as old as Tom. How old is Tom?
    5·1 answer
  • Megan borrowed $3,700 from her parents for 3 years at an annual simple interest rate of 1%. How much interest will she pay if sh
    12·1 answer
  • How do you write 3/6 in the simplest form
    13·1 answer
  • Use the diagram and the value of x to find the measures of BCE and ECF.
    14·1 answer
  • The length of the shorter side of a parallelogram is 29 cm. Perpendicular line segment, which goes through the point of intersec
    15·1 answer
  • The value of y varies directly with x, and y = 104 when x = 13. Find y when x = 2.5. HELP PLEASE
    5·2 answers
  • 40% of students have brown eyes 10 have brown eyes how many atudents in the class
    11·2 answers
  • 2x + 8 = -4 solve for c<br> Show work please
    11·1 answer
  • Please help ill give brainliest
    9·2 answers
  • I need help on this to bring my grade up
    9·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!