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
Alex17521 [72]
3 years ago
13

Solve the initial value problem y′+y=f(t),y(0)=0 where f(t)={1,−1, if t<4 if t≥4 Use h(t−a) for the Heaviside function shifte

d a units horizontally.
Mathematics
1 answer:
Anton [14]3 years ago
4 0

Looks like the function on the right hand side is

f(t)=\begin{cases}1&\text{for }t

We can write it in terms of the Heaviside function,

h(t-a)=\begin{cases}1&\text{for }t\ge a\\0&\text{for }t>a\end{cases}

as

f(t)=h(t)-2h(t-4)

Now for the ODE: take the Laplace transform of both sides:

y'(t)+y(t)=f(t)

\implies s Y(s)-y(0)+Y(s)=\dfrac{1-2e^{-4s}}s

Solve for <em>Y</em>(<em>s</em>), then take the inverse transform to solve for <em>y</em>(<em>t</em>):

(s+1)Y(s)=\dfrac{1-e^{-4s}}s

Y(s)=\dfrac{1-e^{-4s}}{s(s+1)}

Y(s)=(1-e^{-4s})\left(\dfrac1s-\dfrac1{s+1}\right)

Y(s)=\dfrac1s-\dfrac{e^{-4s}}s-\dfrac1{s+1}+\dfrac{e^{-4s}}{s+1}

\implies y(t)=1-h(t-4)-e^{-t}+e^{-(t-4)}h(t-4)

\boxed{y(t)=1-e^{-t}-h(t-4)(1-e^{-(t-4)})}

You might be interested in
Wants to create a path using pebbles. She has 8 bas
frez [133]
The answer to that will be the letter c , 24ft
8 0
3 years ago
Pat made a total of 48 pottery plates and cups. if she made twice as many plates as cups, how many plates did she make?
ddd [48]
If C stands for cups, solve for C

48 - 2c = 0
    l
subtract 48 from each side.
    l
2c=-48
    l
divide 48 by 2 --->  24.



3 0
3 years ago
Read 2 more answers
Directions: Write an integer to model each situation.
Leni [432]

Step-by-step explanation:

tvt67tvyy8vy8vt67vt7v6vt67yvtv

8 0
3 years ago
Please help me!!! I will make you brainiest!!! How does the graph of y=2x+4 compare to the graph of y=x+4
Aloiza [94]

Answer:

ALGUIEN PARA COJER?

TENGO 20 PERRO

7 0
3 years ago
Read 2 more answers
Maureen and her roommates ate 1/8 of a pint of ice cream on Friday night and 3/4 of a pint of ice cream on Saturday night. How m
PilotLPTM [1.2K]

Answer:

The answer is 7/8

Step-by-step explanation:

3/4 is the same as 6/8 so 6/8 plus 1/8 equals 7/8.

5 0
3 years ago
Read 2 more answers
Other questions:
  • How do I do it! Answer pls givin the brainliest
    6·2 answers
  • What is the lateral area of the cone to the nearest whole number? The figure is not drawn to scale.
    5·2 answers
  • Simplify 5(9+3) - 4x3 =
    15·2 answers
  • In Central City, Elm Street and Maple Street are parallel to one another. Oak Street crosses both Elm Street and Maple Street as
    14·1 answer
  • The two triangles are similar.
    7·1 answer
  • Celine and Arlene shared $400. Celine received $50 more than Arlene. How much money did Arlene receive?
    12·1 answer
  • Determine if the two triangles are similar. If they are similar, then which Triangle Similarity Theorem proves they are similar?
    6·1 answer
  • The scale of a map is 3 ft = 84 miles<br> Map:4.5<br> Actual-
    8·1 answer
  • A theater sells its reserved seats for $50 and on average sells 40 reserved seats per show. It has calculated that for every $1
    7·1 answer
  • For each value of y, determine whether it is a solution to 2y&gt; 18.<br>​
    6·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!