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
Luden [163]
1 year ago
10

Initial value problems dy/dx+2y=3. Y(0)=1

Mathematics
1 answer:
Pavel [41]1 year ago
3 0

The initial value equation is y = \frac 12(3 - e^{-2x})

<h3>How to solve the initial value?</h3>

The equation is given as:

\frac{dy}{dx} +2y = 3

Where

Y(0) = 1

Subtract 2y from both sides in the equation

\frac{dy}{dx}  = -2y + 3

Rewrite as:

\frac{dy}{-2y + 3}  =  dx

Integrate both sides of the equation

-\frac 12\ln|-2y + 3| = x + C_o

Multiply through by -2

\ln|-2y + 3| = -2x + C_1

Take the exponent of both sides

-2y + 3 = Ce^{-2x

Next, we solve for C under the initial condition Y(0) = 1.

This gives

-2(1) + 3 = Ce^{-2 * 0

Evaluate

-2 + 3 = C

Solve for C

C = 1

Substitute C = 1 in -2y + 3 = Ce^{-2x

-2y + 3 = e^{-2x

Next, we solve for y

y = \frac 12(3 - e^{-2x})

Hence, the initial value equation is y = \frac 12(3 - e^{-2x})

Read more about initial value at:

brainly.com/question/16945606

#SPJ1

You might be interested in
Dominic is driving on a long road trip. He currently has 10 gallons of gas in his car. Each hour that he drives, his car uses up
zhuklara [117]

Answer:

in three hours he would have used up 3.75 gallons of gas. He would have 6.25 gallons of gas left in his tank after driving 3 hours.

Step-by-step e

5 0
3 years ago
Christina buys 3 DVDs . 2 of the DVDs cost X+Y . Write an expression that shows the amount the 3 DVDs cost
-BARSIC- [3]

Answer:

3/2(x+y)

Step-by-step explanation:

The cost of 2 DVD is x+y

Divide by 2 to get the cost of one DVD

(x+y) /2

Multiply by 3 to get the cost of 3

3/2(x+y)

7 0
2 years ago
Read 2 more answers
Please someone help me with this!
MaRussiya [10]

The sum of two numbers and their difference is 30.

6 0
2 years ago
A total of 632 tickets were sold for the school play. They were either adult tickets or student tickets. There were 68 fewer stu
STALIN [3.7K]
Answer 384

Explanation
In total 632 and there were either adult or students so
632/2=316
So because it said 68 tickets were sold less for the students I added it to 316
316+68=384

Adults=384

I hope this helps if I’m wrong someone please correct me
3 0
2 years ago
Read 2 more answers
Lyla is shopping for school supplies. She has $20.00 to spend. She plans to buy a package of pens for $4.98. She also wants to b
kifflom [539]
X divided by 30 because it is going down by 30 percent.. :)
7 0
2 years ago
Read 2 more answers
Other questions:
  • Which these numbers cant round to 35<br> 35.6<br> 35.1<br> 350.96<br> 35.001<br> 135.1
    5·1 answer
  • Which of the following represents 5 x to the 4 ninths power in radical form? ninth root of 5 x to the fourth power fourth root o
    10·2 answers
  • How many vertices does the following shape have?
    11·1 answer
  • Somebody please help me with this answer
    8·2 answers
  • What’s the mean,median,mode and range
    6·1 answer
  • James is playing his favorite game at the arcade after playing three times He has eight tokens remaining He initially had 20 tok
    15·2 answers
  • 4y - 7 + 2y = -3 (y - 1 ) -1
    7·2 answers
  • Pls help and no unnecessary typin* I will report
    12·1 answer
  • Can you help me on 16, 17, 18, 19, and 20
    14·2 answers
  • Solve the equation using multiplication or division.
    15·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!