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
soldi70 [24.7K]
3 years ago
12

The differential equation y′′=0 has one of the following two parameter families as its general solution: yyyy=C1ex+C2e−x=C1cos(x

)+C2sin(x)=C1tan(x)+C2sec(x)=C1+C2x Find the solution such that y(0)=2 and y′(0)=10. y(x)=
Mathematics
1 answer:
svet-max [94.6K]3 years ago
5 0

Answer:

y_c = 2 + 10*x

Step-by-step explanation:

Given:

                                                y'' = 0

Find:

- The solution to ODE such that y(0) = 2, y'(0) = 10

Solution:

- Assuming a solution y = Ce^(mt)

So,                                y' = C*me^(mt)

                                    y'' = C*m^2e^(mt)

- Back substitute into given ODE, we get:

                                    y'' = C*m^2e^(mt) = 0

                                    e^(mt) can not be equal to zero

- Hence,                       m^2 = 0

                                     m = 0 , 0 - (repeated roots)

- The complimentary function for repeated roots is:

                                    y_c = (C1 + C2*x)*e^(m*t)

                                    y_c = C1 + C2*x  

- Evaluate @ y(0) = 2

                                    2 = C1 + C2*0

                                    C1 = 2

-Evaluate @ y'(0) = 10

                                    y'(t) = C2 = 10

Hence,                         y_c = 2 + 10*x

You might be interested in
Simplify h + h + h , I really need help
lyudmila [28]
3h

Explanation:

Add them
4 0
3 years ago
Read 2 more answers
PLEASE I NEED TO TURN THIS IN TOMORROW I NEED HELP PLEASE HELP ME
mart [117]

Answer: \sum_{n=1}^{5}4^n=1364

Step-by-step explanation:

Since we have given that

\sum_{n=1}^{5}4^n

Now, we know the rule for summation , we'll apply this ,

\sum_{n=1}^{5}4^n\\=4^1+4^2+4^3+4^4+4^5\\

Now, it becomes geometric progression, so we us the formula for sum of terms in g.p. which is given by

S_n=\frac{a(r^n-1)}{r-1}\\\\\text{where 'a' is the first term and 'r' is the common ratio}

So, our equation becomes ,

a=4 \\\\r=\frac{a_2}{a_1}=\frac{4^2}{4}=4\\\\S_5=\frac{4(4^5-1)}{4-1}\\\\S_5=1364

Hence ,

\sum_{n=1}^{5}4^n=1364

7 0
3 years ago
Read 2 more answers
How to solve it and the formula to solve it
notsponge [240]

i) u + 3 V

1 by 2 + 3 *minus 2

1 by 2 -6

1 - 12 by 2

- 11 by 2

ii) - 3 * 1 by 2 + 2 * -2 + 3 by 4

minus 19 by 4

7 0
3 years ago
2(x−3)=8(x−6) what is x?
uysha [10]

Answer: x = 7

Step-by-step explanation:

2x - 6 = 8x - 48

+48

2x + 42 = 8x

-2x

42 = 6x

/6

7 = x

4 0
3 years ago
Read 2 more answers
A survey given to consumers leaving a supermarket three days before Thanksgiving asked whether turkey would be part of the Thank
timofeeve [1]

Answer:

(0.1392,0.1466)

Step-by-step explanation:

Given that a survey given to consumers leaving a supermarket three days before Thanksgiving asked whether turkey would be part of the Thanksgiving meal

People surveyed = 182

claimed not eating turkey = 26

Sample proportion = \frac{26}{182} \\=0.1429

Std error =\sqrt{\frac{pq}{n} } \\=0.0260

Margin of error = 1.96*SE=0.00378

Confidence interval = (0.1429-0.0037,0.1429+0.0037)\\=(0.1392,0.1466)

5 0
3 years ago
Other questions:
  • Answer problems. Really need help
    9·1 answer
  • For what value of x will 55 and x have the mean (average) as 67
    6·2 answers
  • If you drive 168 miles and use 7 gallons of gas, what is your rate of gas consumption?
    5·1 answer
  • HELP WITH PROBABILITY PWEASEEE <br> (4 questions)
    8·1 answer
  • 2(x + 2) + 3x = 2(x + 1) + 1
    11·1 answer
  • People preferred berry blast by 780 compared to 220 who preferred Melon drink. Find the ratio
    9·2 answers
  • Could it be a proportional function?
    9·1 answer
  • What is the greatest common factor (GCF) of 45 and 63?
    9·1 answer
  • Marco has a sandbox that is 3 1/2 feet long, 1/2 feet wide, and foot deep. How
    12·1 answer
  • The Si Unit for velocity is km/h
    7·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!