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
Dmitrij [34]
2 years ago
13

1) Find the general solution to the following differential equation x^3•y’- y = 0

Mathematics
1 answer:
maxonik [38]2 years ago
6 0

Answer:

y(x) = c_1 e^(-1/(2 x^2))

Step-by-step explanation:

Solve the separable equation x^3 (dy(x))/(dx) - y(x) = 0:

Solve for (dy(x))/(dx):

(dy(x))/(dx) = y(x)/x^3

Divide both sides by y(x):

((dy(x))/(dx))/y(x) = 1/x^3

Integrate both sides with respect to x:

integral((dy(x))/(dx))/y(x) dx = integral1/x^3 dx

Evaluate the integrals:

log(y(x)) = -1/(2 x^2) + c_1, where c_1 is an arbitrary constant.

Solve for y(x):

y(x) = e^(-1/(2 x^2) + c_1)

Simplify the arbitrary constants:

Answer:  y(x) = c_1 e^(-1/(2 x^2))

You might be interested in
Please help!!
enot [183]

Since g(h(x))=h(g(x))= x, hence functions h and g are inverses of each other

Given the functions expressed as:

h(x) =\sqrt{2x+2}\\g(x)\frac{x^2-2}{2}  \\

In order to check whether they are inverses of each other, we need to show that h(g(x)) = g(h(x))

Get the composite function h(g(x))

h(g(x))=h(\frac{x^2-2}{2} )\\h(g(x))=\sqrt{2(\frac{x^2-2}{2} )+2}\\h(g(x))=\sqrt{x^2-2+2} \\h(g(x))=\sqrt{x^2}\\h(g(x))=x

Get the composite function g(h(x))

g(h(x))=\frac{(\sqrt{2x+2} )^2-2}{2} \\g(h(x))=\frac{2x+2-2}{2}\\g(h(x))=\frac{2x}{2}\\g(h(x))=x

Since g(h(x))=h(g(x))= x, hence functions h and g are inverses of each other

Learn more on inverse functions here; brainly.com/question/14391067

7 0
2 years ago
Read 2 more answers
Mr. Smith wants to figure out which fast food restaurant is the most popular
hichkok12 [17]
I believe it is biased
6 0
3 years ago
Look at this graph:
Anton [14]

Answer:

3/2

Step-by-step explanation:

slope=rise/run=30/20=3/2

5 0
2 years ago
State the missing angle
Anettt [7]

Answer:

  • zhshhunvsisiiniabiwbgihwqnowowjwg gap
6 0
3 years ago
Read 2 more answers
Just before leaving on the trip, two of Eric’s friends have a family emergency and cannot go. What is each person’s share of the
Vesnalui [34]

Answer: $2.67 per person

Step-by-step explanation: Well hello again, so the question said two of his friends had an emergency now there are three people left going to New York including Eric himself. So, the equation is 8 ÷ 3 = ?. Now we solve the equation 8 ÷ 3 = ? which is $2.67.

8 0
2 years ago
Other questions:
  • Robert drives 45 miles in 3 hours from New York City to New Jersey. How far will he drive in 5 hours?
    10·1 answer
  • HELP ASAP
    13·1 answer
  • Levi borrowed $7129 at 4% simple interest for 6 months. How much will the interest amount to? What is the total amount that Levi
    7·1 answer
  • *The length of the shorter altitude and the shorter side of a parallelogram are 9cm and 82 cm. The length of a longer diagonal i
    9·1 answer
  • (4a^3)(5a)^2 with work
    14·1 answer
  • Question 9 (1 point)
    6·1 answer
  • Khan academy circles unit test
    5·1 answer
  • The orbit of Pluto can be modeled by the equation {x^2}/{39.5^2} + {y^2}/{38.3^2 } = 1, where the units are astronomical units.
    12·1 answer
  • Solve −163 = −25d .
    15·1 answer
  • a number is chosen at random from the numbers 1 to 100. what is the probability that the number is divisible by 5?
    8·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!