Solve the homogeneous equations. First put the equation in the form of a homogeneous equation. (xe y/x
Question:
Solve the homogeneous equations. First put the equation in the form of a homogeneous equation.
(xey/x + y) dx - x dy = 0
Transcribed Image Text:
A first-order differential equation of the form dy dx is called homogeneous. It can be transformed into an equation whose variables are separable by defining the new variable v = y/x. Then, y = vx and dy dx dx du + = v + x² Substitution into the original differential equation and collecting terms with like variables then gives the separable equation dx dv v - F(v) 0. After solving this separable equation, the solution of the original equation is obtained when we replace v by y/x.
Fantastic news! We've Found the answer you've been seeking!
Step by Step Answer:
Answer rating: 50% (4 reviews)
We have the differential equation xeyx y dx x dy 0 Dividing both sides by x dx we get ...View the full answer
Answered By
Mary Boke
I have teached the student upto class 12th as well as my fellow mates.I have a good command in engineering,maths and science.I scored 90+ marks in 10th and 12th in maths.
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
-
Solve the homogeneous equations. First put the equation in the form of a homogeneous equation. (x + y) dy + (x - y) dx = 0 A first-order differential equation of the form dy dx is called homogeneous....
-
Solve the homogeneous equations. First put the equation in the form of a homogeneous equation. x 2 dy + (y 2 - xy) dx = 0 A first-order differential equation of the form dy dx is called homogeneous....
-
In Exercises solve the homogeneous differential equation in terms of x and y. A homogeneous differential equation is an equation of the form M(x, y) dx + N(x, y) dy = 0, where M and N are homogeneous...
-
QUESTION Mahkota Oil Sdn Bhd has been involved in the palm oil processing industry for several years. It has a steady market and competing successfully with other more expensive vegetable oil...
-
1. When the Steeles decide to replace the family car, what factors should they consider when deciding whether to purchase a new or a used car? 2. Why are the monthly lease payments typically lower...
-
Management of Shreveport Community Hospital has decided to allocate the budgeted costs of its three support departments (administration, public relations, and maintenance) to its three operating...
-
The rod has a circular cross section with a moment of inertia \(I\). If a vertical force \(\mathbf{P}\) is applied at \(A\), determine the vertical displacement at this point. Only consider the...
-
ABC, cost hierarchy, service (CMA, adapted) Vineyard Test Laboratories does heat testing (HT) and stress testing (ST) on materials and operates at capacity. Under its current simple costing system,...
-
Rudder Co. is authorized to issue 10,000 shares of $5 par common stock and enters into the following stock (treasury stock) transactions. Required: A. Record the journal entry for each transaction....
-
You are an equity analyst at an investment bank. You have been asked to perform valuation of Novice Ltd., a company that specialises in the media industry. You have been provided with the following...
-
Show that the second-order differential equation y = F(x, y, y) can be reduced to a system of two first-order differential equations Can something similar be done to the nth-order differential...
-
a. Identify the equilibrium values. Which are stable and which are unstable? b. Construct a phase line. Identify the signs of y and y. c. Sketch several solution curves. y = y, y > 0
-
The following is a partial list of the accounts for Boot Company for the year ended December 31, 2017, in alphabetical order: Dr.(Cr.) Common shares...
-
What is the objective of SAS No. 78?
-
How does the Sarbanes-Oxley Act of 2002 affect managements responsibility for internal controls?
-
Explain how an IT environment affects the segregation of functions
-
The sponsor of a project to move the loan processing system from C++ to the intranet is deciding whether the project should continue or be scrapped. The project has been plagued with issues. So far,...
-
Explain whether authorizations are necessary in a computer environment.
-
1. Define pure economic rent. 2. Explain why the supply curve of land can be upwardsloping when there is a fixed quantity of land in the world. 3. Define artificial rent. 4. Define real rent. 5....
-
Consider the function f and its graph. a. Estimate the zeros of the area function b. Estimate the points (if any) at which A has a local maximum or minimum. c. Sketch a graph of A, for 0 x 10,...
-
After a 5.5-mg injection of dye, the readings of dye concentration, in mg/L, at two-second intervals are as shown in the table. Use Simpsons Rule to estimate the cardiac output. c(t) c(t) 0.0 10 4.3...
-
The density function f(x) = e 3-x /(1 + e 3-x ) 2 is an example of a logistic distribution. (a) Verify that f is a probability density function. (b) Find P(3 < X < 4). (c) Graph f. What does the mean...
-
Let f (x) = c/(1 + x 2 ). (a) For what value of c is f a probability density function? (b) For that value of c, find P (-1 < X < 1).
-
5. A person wants to pay off a debt of $450,000 with 11 equal semiannual payments of $37,000 and a final one for the remaining amount. If the interest rate is 18% convertible semiannually, how much...
-
Discuss the four key questions managers need to answer when using the balanced scorecard to develop strategic objectives.
-
Answer the following questions using the following case framework: DeBeers's Diamond Dilemma Case Study Link to the case:...
Study smarter with the SolutionInn App