X(x-1) y’ + y(y-1) using separating differencialne rovnice



Answer to a math question X(x-1) y’ + y(y-1) using separating differencialne rovnice

Expert avatar
68 Answers
To solve the differential equation X(x-1)y' + y(y-1) = 0 using separation of variables, we first rewrite it in the form:

X(x-1)y' + y(y-1) = 0

\frac{X(x-1)}{y(1-y)} dy = -dx

Now, we will separate variables and integrate:

\int \frac{X(x-1)}{y(1-y)} dy = \int -dx

\int \frac{1}{y(1-y)} dy = -\int \frac{1}{X(x-1)} dx

\int \left(\frac{1}{y} + \frac{1}{1-y}\right) dy = - \frac{1}{X} \int \frac{1}{x-1} dx

\int \left(\frac{1}{y} + \frac{1}{1-y}\right) dy = - \frac{1}{X} \ln|x-1| + C

Integrate with respect to y:

\ln|y| - \ln|1-y| = - \frac{1}{X} \ln|x-1| + C

Simplify and rewrite in terms of y:

\ln\left|\frac{y}{1-y}\right| = - \frac{1}{X} \ln|x-1| + C

Exponentiate both sides to eliminate the logarithms:

\left|\frac{y}{1-y}\right| = C (x-1)^{-X}

Solving for y:

\frac{y}{1-y} = \pm C (x-1)^{-X}

y = \frac{C(x-1)^{-X}}{1 \pm C(x-1)^{-X}}

Therefore, the solution to the differential equation is:

\boxed{y = \frac{C(x-1)^{-X}}{1 \pm C(x-1)^{-X}}}

Frequently asked questions (FAQs)
Math Question: Find the extreme values of the function f(x) = x^3 - 3x^2 + 2 on the interval [-2, 3].
What is the value of f(x) if f(x) = logβ‚‚ x?
What is the product of the mixed number 3 1/4, the factored number 8 Γ— 5 Γ— 3, and the real number 2.5?
New questions in Mathematics
A person who weighs 200 pounds on earth would weigh about 32 pounds on the moon. Find the weight of a person on earth who would weigh 15 pounds on the moon.
what is 9% of 307
2x-y=5 x-y=4
I) Find the directional derivative of 𝑓(π‘₯, 𝑦) = π‘₯ sin 𝑦 at (1,0) in the direction of the unit vector that make an angle of πœ‹/4 with positive π‘₯-axis.
In a store there are packets of chocolate, strawberry, tutti-frutti, lemon, grape and banana sweets. If a person needs to choose 4 flavors of candy from those available, how many ways can they make that choice?
What is the appropriate measurement for the weight of an African elephant?
TEST 123123+123123
On+January+10+2023+the+CONSTRUCTORA+DEL+ORIENTE+SAC+company+acquires+land+to+develop+a+real estate+project%2C+which+prev%C3% A9+enable+50+lots+for+commercial+use+valued+in+S%2F+50%2C000.00+each+one%2C+the+company+has+as+a+business+model+generate+ cash+flow+through%C3%A9s+of+the+rental%2C+so+47%2C+of+the+50+enabled+lots+are+planned to lease+47%2C+and+ the+rest+will be%C3%A1n+used+by+the+company+for+management%C3%B3n+and+land+control
36 cars of the same model that were sold in a dealership, and the number of days that each one remained in the dealership yard before being sold is determined. The sample average is 9.75 days, with a sample standard deviation of 2, 39 days. Construct a 95% confidence interval for the population mean number of days that a car remains on the dealership's forecourt
The annual real property tax liability for a residential property is $4302 and has been paid by the seller in advance of closing. Using the 30-day month/260-day year method what will be the tax proration entry on the settlement statement round to the nearest dollar for a closing on Oct. 26 if the buyer owns the day of closing? a. $3525 credit to the buyer and $777 debit to the seller b. $777 debit to the buyer and $3525 debit to the seller c. $777 credit to the buyer and $777 debit to the seller d. $3525 debit to the buyer and $3525 credit to the seller *Can anyone help with this? I am studying for my real estate exam and am having trouble with some of the calculations :)
prove that for sets SS, AA, BB, and CC, where AA, BB, and CC are subsets of SS, the following equality holds: (Aβˆ’B)βˆ’C=(Aβˆ’C)βˆ’(Bβˆ’C)
A psychologist is investigating the levels of test anxiety in various university courses. Anxiety is measured on a scale ranging from 0 to 100, where 0 indicates the complete absence of anxiety and 100 represents an extreme level of anxiety. From the data obtained, it has been discovered that the psychology score is triple that of nursing, and in turn, the latter has a score 10 points lower than the nutrition major. Furthermore, the score in the veterinary degree is 15 points higher than that of nutrition. Finally, if we add the scores of all the races, we will obtain a total of 173 points. Pose the equation that represents the situation described in the previous problem and determine: What is the score that psychology obtained regarding its anxiety level before the exams?
A post office has three categories of letters: 60% are from businesses, 30% are individual mail, and the remaining 10% are government mail. 5% of the letters from businesses have address errors, 10% of the individual mail has address errors, while 1% of the government mail has address errors. If we receive a letter with an address error, what is the probability that it is individual mail?"
A confidence interval for a population mean has a margin of error of 3.5. a. Determine the length of the confidence interval. b. If the sample mean is 47.8 ​, obtain the confidence interval. a. The length of the confidence interval is?
simplify w+[6+(-5)]
The inner radius of a spherical ball is 13 cm. How many liters of air are in it? Justify your answer!
a coffee shop has 9 types of creamer and 11 types of sweetener. In how any ways can a person make their coffee?
draw the condensed formula fpr 3,3,4 triethylnonane