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
Dahasolnce [82]
3 years ago
12

Find an explicit solution of the given initial-value problem. (1 + x4) dy + x(1 + 4y2) dx = 0, y(1) = 0

Mathematics
1 answer:
MissTica3 years ago
5 0

Answer:

a solution is 1/2 *tan⁻¹ (2*y) = - tan⁻¹ (x²) + π/4

Step-by-step explanation:

for the equation

(1 + x⁴) dy + x*(1 + 4y²) dx = 0

(1 + x⁴) dy  = - x*(1 + 4y²) dx

[1/(1 + 4y²)] dy = [-x/(1 + x⁴)] dx

∫[1/(1 + 4y²)] dy = ∫[-x/(1 + x⁴)] dx

now to solve each integral

I₁= ∫[1/(1 + 4y²)] dy = 1/2 *tan⁻¹ (2*y) + C₁

I₂=  ∫[-x/(1 + x⁴)] dx

for u= x² → du=x*dx

I₂=  ∫[-x/(1 + x⁴)] dx = -∫[1/(1 + u² )] du = - tan⁻¹ (u) +C₂ =  - tan⁻¹ (x²) +C₂

then

1/2 *tan⁻¹ (2*y) = - tan⁻¹ (x²) +C

for y(x=1) = 0

1/2 *tan⁻¹ (2*0) = - tan⁻¹ (1²) +C

since tan⁻¹ (1²) for π/4+ π*N and tan⁻¹ (0) for  π*N , we will choose for simplicity N=0 . hen an explicit solution would be

1/2 * 0 = - π/4 + C

C= π/4

therefore

1/2 *tan⁻¹ (2*y) = - tan⁻¹ (x²) + π/4

You might be interested in
If a/4=2, what does a equal
Anni [7]
8 because inverse operations indicate that 4x2=8
6 0
3 years ago
What are the roots of f(x)=x2-48
Tcecarenko [31]
I do believe that would be x=6 and x=-8
5 0
3 years ago
Read 2 more answers
Triangle B = 10cm <br>H = 4cm<br>area =​
charle [14.2K]

Answer:

I think it's 20

Step-by-step explanation:

10x4÷2 because vase times height,the divide by 1/2 which it 2 so answer is 20

3 0
3 years ago
Graph f(x)=2x−1 and g(x)=−x+5 on the same coordinate plane.
Stels [109]
The solution is when the two functions meet x=2. The green function is f(x), and the red is g(x).

4 0
3 years ago
Read 2 more answers
A student dropped a textbook from the top floor of his dorm and it fell according to the formula s(t) = −16t 2 + 8√t , where t i
Sidana [21]

Answer:

<h2>-29.61m/s</h2>

Step-by-step explanation:

Given the distance of fall of the student in term of the time t expressed by the equation s(t) = −16t² + 8√t, to get the average speed of fall of the pencil after 2.8 secs, we will need to differentiate the given function first since Velocity is the change in distance of a body with respect to time i.e

V = d(s(t))/dt

s(t) = −16t² + 8t^1/2

V = -32t+1/2(8)t^(1/2 - 1)

V = -32t+4t^-1/2

The average speed of the fall Using the fact that the pencil hit the ground in exactly 2.8 seconds, will be gotten by substituting t = 2.8 into the resulting equation.

V = -32t+4(2.8)^-1/2

V = -32t+4/√2.8

V = -32+4/1.6733

V = -32+2.391

v = -29.61m/s

<em>Hence the average speed of the fall is -29.61m/s</em>

3 0
3 years ago
Other questions:
  • Write the answer in scientific notation
    10·1 answer
  • julia woke up at 7:05 A.M. She left for school at 7:25 A.M. How many degrees did the minute hand on the clock turn from the time
    5·1 answer
  • Choose the graph. Find the angle of theta if secθ=-13/5 and tanθ is negative.
    12·1 answer
  • How much longer is the big arc than the small arc. Give the answer to 1 decimal place
    12·1 answer
  • Krutika was thinking of a number. Krutika doubles it and gets an answer of 26.5. What was the original number?
    9·2 answers
  • What is the surface area of this rectangular prism?<br><br> 5 ft<br> 4 ft<br> 12 ft
    14·2 answers
  • Find the surface area of this rectangular pyramid. 4.5 in 3 in 4 in 5 in​
    5·2 answers
  • Please answer correctly !!!!! Will mark Brianliest !!!!!!!!!!!!!!
    13·1 answer
  • Shaun is painting a fence. After finishing three-eighths of the length of the fence he finds that
    5·2 answers
  • Carlos wants to have an average of
    6·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!