Solve the Bernoulli equations. xy + y = y -2 A Bernoulli differential equation is of the
Question:
Solve the Bernoulli equations.
xy′ + y = y-2
Transcribed Image Text:
A Bernoulli differential equation is of the form dy dx + P(x)y = Q(x)y". Observe that, if n = 0 or 1, the Bernoulli equation is linear. For other values of n, the substitution u = yl-" transforms the Bernoulli equation into the linear equation du dx For example, in the equation dy dx or, equivalently, + (1 − n)P(x)u = (1 − n)Q(x). = we have n = 2. so that u = y¹-2 = y¹ and du/dx = -y²dy/dx. Then dy/dx = -y² du/dx = -u² du/dx. Substitution into the original equation gives =e^u² -2 du dx - y = exy² du dx +u = −ex. This last equation is linear in the (unknown) dependent variable u.
Fantastic news! We've Found the answer you've been seeking!
Step by Step Answer:
Answer rating: 100% (2 reviews)
ANSWER To solve the given Bernoulli equation we first need to check if it is in the s...View the full answer
Answered By
Chandrasekhar Karri
I have tutored students in accounting at the high school and college levels. I have developed strong teaching methods, which allow me to effectively explain complex accounting concepts to students. Additionally, I am committed to helping students reach their academic goals and providing them with the necessary tools to succeed.
0.00
0 Reviews
10+ Question Solved
Related Book For
Thomas Calculus Early Transcendentals
ISBN: 9780321884077
13th Edition
Authors: Joel R Hass, Christopher E Heil, Maurice D Weir
Question Posted:
Students also viewed these Mathematics questions
-
On October 1 of the current year a corporation sold, at par plus accrued interest, $1,000,000 of its 12% bonds, which were dated July 1 of this year. What amount of bond interest expense should the...
-
Solve this system of three equations with three unknowns using EES: 2x y + z = 5 3x2 + 2y = z + 5 Xy + 2z = 8
-
Solve each system of equations by letting X = 1 /x, Y = 1/y, and Z = 1/z. (a) (b) 12 _ 12 y 4 3 y 3 4 4 10 3 13 -8 2 ||
-
The following information provides details of costs, volume and cost drivers for a particular period in respect of ABC plc, a hypothetical company: ( Details Direct Material $25 Cost Direct Labor 4/3...
-
Compare a regular cash dividend with a periodic share repurchase. Which has greater appeal to you? Explain.
-
Tacoma Inc. bottles and distributes spring water. On June 12 of the current year, Tacoma Inc. reacquired 15,000 shares of its common stock at $48 per share. On August 10, Tacoma Inc. sold 9,000 of...
-
Discuss the characteristics of effective feedback.
-
Maui Outfitters Corporation manufactures and distributes leisure clothing. Selected transactions completed by Maui Outfitters during the current fiscal year are as follows: Feb 19. Split the common...
-
How is the amount of research renewed and when is it renewed? Explain.
-
A U.S. company owns an 80% interest in a company located on Mars. Martian currency is called the Martian Credit. During the year the parent company sold inventory that had cost $24,000 to the...
-
How many seconds after the switch in an RL circuit is closed will it take the current i to reach half of its steady-state value? Notice that the time depends on R and L and not on how much voltage is...
-
Obtain a slope field and add to it graphs of the solution curves passing through the given points. y = y(x + y) with a. (0, 1) b. (0, -2) c. (0, 1/4) d. (-1, -1)
-
How much power relative to this decision did Mary, Jack, and the president of Standard Software possess, and what type of power was it?
-
How many degrees of freedom are there in a three-element model of a fixed-free bar?
-
If \(P(0)=0.5\) for a normalized random variable, the probability distribution follows the Gaussian distribution. Indicate whether the statement presented is true or false. If true, state why. If...
-
The probability distribution function is the derivative of the probability density function. Indicate whether the statement presented is true or false. If true, state why. If false, rewrite the...
-
The Weiner-Khintchine equations imply that the autocorrelation function is the Fourier transform of the power spectral density. Indicate whether the statement presented is true or false. If true,...
-
A stationary process is one in which a representative sample of ensemble measurements can be used for the entire process. Indicate whether the statement presented is true or false. If true, state...
-
Why is it better for theories to be judged by how accurately they predict than by how they sound to us?
-
For the following exercises, write the polynomial function that models the given situation. Consider the same rectangle of the preceding problem. Squares of 2x by 2x units are cut out of each corner....
-
Use (a) the Trapezoidal Rule, (b) the Midpoint Rule, and (c) Simpsons Rule to approximate the given integral with the specified value of n. (Round your answers to six decimal places.) /2 V1 + cos x...
-
Use (a) the Trapezoidal Rule, (b) the Midpoint Rule, and (c) Simpsons Rule to approximate the given integral with the specified value of n. (Round your answers to six decimal places.) '4 sin x dx, n...
-
Use (a) the Trapezoidal Rule, (b) the Midpoint Rule, and (c) Simpsons Rule to approximate the given integral with the specified value of n. (Round your answers to six decimal places.) | ell# dx, *3 ...
-
1. A man of a mass 70 kg steps forward out of a boat and onto the nearby river bank with a velocity, when he leaves the boat, of 2.5 m.s relative to the ground. The boat has a mass of 400 kg and was...
-
d) Determine the horizontal position x of the cart at t = 9.0 s if the cart is located at x = 2.0 m at t = 0. Show your work. e) On the axes below, sketch a graph of the cart's acceleration (a) as a...
-
How much horsepower does a 1 2 , 0 0 0 - pound thrust jet engine produce flying at 2 5 0 knots?
Study smarter with the SolutionInn App