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
kogti [31]
3 years ago
10

Solve the differential equation. (y^2 + xy^2)y' = 1

Mathematics
1 answer:
stira [4]3 years ago
6 0
(y^2 + xy^2)y' = 1  \ \Rightarrow\ (y^2 + xy^2)\frac{dy}{dx}= 1  \ \Rightarrow\\ \\
y^2(1 + x) \frac{dy}{dx} = 1  \ \Rightarrow\ y^2 dx = \frac{dx}{1 + x}\ \Rightarrow \\ \\
\int y^2 dx =\int \frac{dx}{1 + x} \ \Rightarrow\ \frac{1}{3}y^3 = \ln|1+x| + C\ \Rightarrow \\ \\
y^3 = 3 \ln|1 + x| + 3C\ \Rightarrow\ y = \sqrt[3]{3\ln|1+x| + K},\ \text{where $K = 3C$}

You might be interested in
PLEASE HELPPP!!
olga55 [171]

Answer:

3(8-4x) < 6(x-5)

24-12x < 6x-30

24+30 < 6x+12x

54 < 18x

54\18 < x

3 < x

It means the ans is option no. b

6 0
3 years ago
Read 2 more answers
"Express as a mixed numeral: 39/8" is a problem found in a fifth-grade arithmetic textbook. This problem is BEST solved through:
Scilla [17]

Answer:

  c.  an algorithm

Step-by-step explanation:

Most math problems are best solved using an algorithm. Certainly, converting numbers from one form to another is easily done that way.

_____

The integer part is the whole-number quotient of the division. The fractional part is the remainder divided by the denominator:

  39/8 = 32/8 + 7/8 = 4 7/8

5 0
3 years ago
CJ = 3x + 6,<br> CT = 37, and<br> JT = 3x + 7<br> Find JT.
GrogVix [38]

Answer:

JT=19

Step-by-step explanation:

3x+6+3x+7=37

6x+6+7=37

6x+13=37

    -13  -13

6x=24

6x/6=24/6

x=4

3x+7

3(4)+7

12+7

JT=19

3 0
3 years ago
Factor the expression using<br>the greatest common factor:<br>27x + 45​
Ghella [55]

Answer:

The GCF should be 9

Step-by-step explanation:

8 0
3 years ago
Read 2 more answers
Solve. 4x + 10= 2x – 14
hammer [34]

Answer:

x = -12

Step-by-step explanation:

Step 1: Subtract 2x from both sides

2x + 10 = -14

Step 2: Subtract 10 from both sides

2x = -24

Step 3: Divide both sides by 2

x = -12

8 0
3 years ago
Read 2 more answers
Other questions:
  • The temperature at any random location in a kiln used for manufacturing bricks is normally distributed with a mean of 1000°f and
    13·1 answer
  • Anybody have a real answer to the question?
    7·1 answer
  • What is the reduced fraction of 27/8
    15·1 answer
  • One vertex of an equilateral triangle is at the origin and the other vertex is at (3,4)
    12·2 answers
  • The sum of two numbers s 21. The larger number is 6 less than twice the smaller number. Find the two numbers
    11·2 answers
  • Last year, Leron worked 8 hours a day,5 days a week, for 50 weeks. He earned $28 per hour. How much dd he earn for the entire ye
    8·1 answer
  • A plane is defined as what type of figure? A. 1-dimensional B. 2-dimensional C. 3-dimensional D. A plane has no dimensions.
    12·1 answer
  • The equation of a line is y=mx+ 4. What is the value of m if the line passes through point (−3, 7)?
    7·2 answers
  • Write an equation that represents the line.<br> Use exact numbers
    9·1 answer
  • 16,047
    7·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!