Question: Verify that x 2 y' + e y = 0 is separable. (a) Write it as e dy = -x dx. (b) Integrate both sides

Verify that x²y' + e^−y= 0 is separable.

(a) Write it as e dy = -x dx. (b) Integrate both sides to obtain e = x + C. (c) Verify that y = ln(x+C) is

(a) Write it as e dy = -x dx. (b) Integrate both sides to obtain e = x + C. (c) Verify that y = ln(x+C) is the general solution. (d) Find the particular solution satisfying y(2) = 4.

Step by Step Solution

★★★★★

3.44 Rating (160 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock

Solving xy ey 0 for y yields y xey a Separating variables in the last eq... View full answer

Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock

Step: 3 Unlock

Students Have Also Explored These Related Calculus 4th Questions!

Let F be an algebraic closure of the field Q of rational numbers and let E F be a splitting field over Q of the set S = { x 2 + a | a Q} so that E is algebraic and Galois over Q (Theorem 3.11). (a)...

Suppose that X is a separable metric space which satisfies the Bolzano-Weierstrass Property, that Y is a complete metric space, and that E is a bounded subset of X. Prove that a function f: E Y is...

Mark each of the following true or false. ___ a. No proper algebraic extension of an infinite field of characteristic p 0 is ever a separable extension. ___ b. If F(a) is totally inseparable over F...

MATH260Week 6 Lab Name: Antiderivatives According to the first part of the fundamental theorem of calculus, the antiderivative reverses the derivative. If f(x) is a derivative, F(x) is the...

Section 8.4 Reading Assignment: Trigonometric Substitution Answer Only Exercise 1, 2, and 3 by using a screenshot provided Calculus Pearson textbook. Make sure you read these three questions very...

Ch 11 Differential Equations 11.2 Slope Fields the only two questions from that section Match each of the slope field segments in (IV)-(VI) with one or more of the differential equations. X...

In this question you will solve the following separable differential equation to give a relationship between x and y, dy 2 y2 with y (0) = 1. da First write this equation in the form P (y) dy = Q(x)...

Hey can you help me my homework Please show and organize your work clearly. Professor finished 70- 90% of the work you just have to finish the work. please please please follow his work 1. Evaluate...

BUSINESS CALCULUS INCOURSE TEST #1 (UNITS 1 & 2) SEMESTER 2 2022 SECTION A Instructions: Attempt ALL questions in this section. 1. Let f(x) be a function; what does it mean to say "f(x) has a limit...

Which of the following bonds offers the highest current yield? a. A 91/2%, 20-year bond quoted at 973/4 b. A 16%, 15-year bond quoted at 1645/8 c. A 51/4%, 18-year bond quoted at 54

Working with others in teams or groups is a common practice in both workplace and academic contexts. Write an essay of 300 words discussing the guidelines to communicate inclusively within the team....

Which of the following is true of the perfectly competitive firm in the short run? (A) The firm earns a normal profit. (B) The firm shuts down if the price falls below average total cost. (C) The...

12.12 Bushey Travel is an online travel agent. Clients can book online or by telephoning the companys headquarters which are located in a business park. Bushey Travel operates as an agency only (i.e....

Determine whether Rolles Theorem applies to the following functions on the given interval. If so, find the point(s) that are guaranteed to exist by Rolles Theorem. f(x) = sin 2x; [0, /2]

Determine the intervals on which the following functions are concave up or concave down. Identify any inflection points. g(t) = ln (3t 2 + 1)

Sketch a complete graph of the following functions. Use analytical methods and a graphing utility together in a complementary way. f(x) = 3x 4 - 44x 3 + 60x 2 (Two different graphing windows may be...

Research the city of Scranton, Pennsylvania. What lead to their serious financial difficulties that may likely lead to bankruptcy? What mistakes were made? How could this been avoided? What is their...

Please draw a hand sketch of the root locus with detailed step by step explaination.

If the expenses are understated by RM5,000, what is the effect on the net income?