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
maw [93]
3 years ago
13

Consider the differential equationy′′+3y′−10y=0.(a) Find the general solution to this differential equation.(b) Now solve the in

itial-value problem corresponding to y(0)=2 and y′(0)=10.
Mathematics
1 answer:
RSB [31]3 years ago
6 0

Answer:

Y= 2e^(5t)

Step-by-step explanation:

Taking Laplace of the given differential equation:

s^2+3s-10=0

s^2+5s-2s-10=0

s(s+5)-2(s+5) =0

(s-2) (s+5) =0

s=2, s=-5

Hence, the general solution will be:

Y=Ae^(-2t)+ Be^(5t)………………………………(D)

Put t = 0 in equation (D)

Y (0) =A+B

2 =A+B……………………………………… (i)

Now take derivative of (D) with respect to "t", we get:

Y=-2Ae^(-2t)+5Be^(5t)   ....................... (E)

Put t = 0 in equation (E) we get:

Y’ (0) = -2A+5B

10  = -2A+5B ……………………………………(ii)

2(i) + (ii) =>

2A+2B=4 .....................(iii)

-2A+5B=10 .................(iv)

Solving (iii) and (iv)

7B=14

B=2

Now put B=2 in (i)

A=2-2

A=0

By putting the values of A and B in equation (D)

Y= 2e^(5t)

You might be interested in
The original price of a toaster is $18.00. If the toaster is marked down 25%, what is the new price?
Alla [95]

Answer:

$13.50

Step-by-step explanation:

First, we got to multiply $18 by 25% or .25

$18 x .25 = $4.50

Lastly, we just subtract $4.50 from $18.

$18 - $4.50 = $13.50

5 0
3 years ago
What is the value of x in the equation x - y = 30, when y = 15?<br> O4<br> O 8<br> O 80<br> O 200
olganol [36]

\frac{1}{5}x -  \frac{2}{3} y = 30  \\

Putting the value of Y = 15

\frac{1}{5} x -  \frac{2}{3}  \times 15 = 30  \\   \frac{1}{5} x = 30  +  10 \\  \frac{1}{5} x = 40 \\ x = 5 \times 40 \\  x = 200

So, X = 200

6 0
2 years ago
Consider m = y2 - y1/ x2 - x1 . Which x1 and x2-values would determine that the line is vertical? Justify your answer
Y_Kistochka [10]

Answer:

x_2=x_1

Step-by-step explanation:

We were given the slope formula;

m=\frac{y_2-y_1}{x_2-x_1}

This line is vertical if the denominator is zero.

That is when x_2-x-1=0

This implies that;

x_2=x_1

Justification;

When x_2=x_1, then, the line passes through;

(x_1,y_1)  and (x_1,y_2)

The slope now become

m=\frac{y_2-y_1}{x_1-x_1}=\frac{y_2-y_1}{0}

The equation of the line is

y-y_1=\frac{y_2-y_1}{0}(x-x_1)

This implies that;

0(y-y_1)=(y_2-y_1)(x-x_1)

0=(y_2-y_1)(x-x_1)

\frac{0}{y_2-y_1}=(x-x_1)

0=(x-x_1)

x=x_1... This is the equation of a vertical line.

3 0
3 years ago
5) 6x + 5y =-15<br><br> Need help it’s writing linear equations!!
Svetach [21]

Answer:

oh this is the topic we are talking on in my class

4 0
3 years ago
Read 2 more answers
Tom plants 3 seeds.
Rasek [7]

Answer:

A. 64/125

B. 124/125.

Step-by-step explanation:

A).  As the events ( germinate or not germinate) are independent we multiply the probabilities.

Prob(All seeds germinate) = 4/5*4/5*4/5 =  64/125.

B). Probability of at least one germinating =  1 - probability that none germinate

Probability of  1 seed not germinating = 1 -45 = 1/5.

So Prob(at least one germinating)

= 1 - (1/5 * 1/5 * 1/5)

= 1 - 1/125

= 124/125.

5 0
3 years ago
Other questions:
  • Which of the following are solutions to the equation below?4x^2-12x+9=5
    8·2 answers
  • The graph of the function f(x) is shown below.
    15·1 answer
  • What is? 1 3/14 - ( -2 1/7) express your answer in the simplest form
    6·1 answer
  • Given a cylinder with
    14·2 answers
  • Select ALL the correct answers.
    5·2 answers
  • Solve a math problem
    11·2 answers
  • If 3(r+300)=6, then what would be the value of r+300-2?
    15·1 answer
  • What is nearest whole number of 14.603
    5·2 answers
  • By which rule are these triangles congruent?<br><br> АА<br> SAS<br> SSA<br> AAS
    13·2 answers
  • - 6/39 simplified. :)​
    15·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!