Check if each of the following ODEs is an exact. If it is not an exact...

Check if each of the following ODEs is an exact. If it is not an exact ﬁnd an integrating factor to make it an exact. Then solve each of the following ODEs.

(e) dx + (x/y−siny)dy = 0

(f) ydx + (2x−ye^y)dy = 0

(g) (3x²y + 2xy + y³)dx + (x² + y²)dy = 0

Solutions

Expert Solution

Colby Messinger answered 1 year ago

Next > < Previous

Related Solutions

Check that the following differential equation is not exact. Find an integrating factor that makes it...

Check that the following differential equation is not exact. Find an integrating factor that makes it exact and solve it. ydx + (3 + 3x-y) dy = 0 __ Solve the initial value problem: (cos xsen x-xy ^ 2) dx + (1-x ^ 2) ydy = 0 if y (0) = 2 __ Solve the initial value problem: y ^ (2) cosx dx + (4 + 5ysenx) dy = 0; y (π / 2) = 1

Solve each of the following ODEs. If initial conditions are given, give the unique solution. d)...

Solve each of the following ODEs. If initial conditions are given, give the unique solution. d) y''' − 5y'' + 2y' + 8y = 0, y(0) = 2, y'(0) = −1, y''(0) = −5 e) y''' + 9y'' + 27y' + 27y = 0, y(0) = 2, y'(0) = 0, y''(0) = 3 a) x^2y'' + xy' + 4y = 0, x > 0 b) x^2y'' − 6y = 0, x > 0, y(1) = y'(1) = 5 c) x^2y''...

Identify the numbers in each of the following statements as measured or exact: (Write a BRIEF...

Identify the numbers in each of the following statements as measured or exact: (Write a BRIEF explanation for how you got your answer.) a. There are 31 students in the laboratory. b. The oldest known flower lived 1.20 x 10/8 yr ago. c. The largest gem ever found, an aquamarine, has a mass of 104 kg. d. A laboratory test shows a blood cholesterol level of 184 mg/dL.

In each of the following situations, Emma is in the exact center of a glass-sided freight...

In each of the following situations, Emma is in the exact center of a glass-sided freight car speeding to the right at a very high speed v relative to you. For each question, explain your reasoning. Emma has a flashlight in each hand and directs them at the front and rear ends of the freight car. She then switches the flashlights on at the same time. In Emma

for each of the following statements, fill in the blanks with an easy to check criterion:...

for each of the following statements, fill in the blanks with an easy to check criterion: a. M is a triangular number if and only if _______ is an odd number. b. N is an odd square if and only if _________ is a triangular number. c. prove that your criteria in a and b are correct.

Find solutions to the following ODEs: • y¨ − y˙ − 2y = t, y(0) =...

Find solutions to the following ODEs: • y¨ − y˙ − 2y = t, y(0) = 0, y˙(0) = 1 • y¨ − 2 ˙y + y = 4 sin(t), y(0) = 1, y˙(0) = 0 • y¨ = t 2 + t + 1 (find general solution only) • y¨ + 4y = t − 2 sin(2t), y(π) = 0, y˙(π) = 1

Find the general solution for the following ODEs. If initial condition is given, solve the initial...

Find the general solution for the following ODEs. If initial condition is given, solve the initial value problem. 3) (D^4 − 13D^2 + 36I)y = 12e^x 4) (D^3 − D^2 − D + I)y = 0, y(0) = 0, Dy(0) = 1, D^2y(0) = 0

Question 1. Find the general solution of the following ODEs a) y′′ − 2y′ − 3y...

Question 1. Find the general solution of the following ODEs a) y′′ − 2y′ − 3y = e−x + 2e3x b) y′′ + y′ + y = x2 + 4 cos x.

Check each of the following that could be classified as products made by an oligopolistic competitor....

Check each of the following that could be classified as products made by an oligopolistic competitor. cigarettes breakfast cereals airlines cotton cell phones motor vehicles (Check each of the correct answers) Game theory suggests that firms in oligopoly: would resist offering a low price because other firms would match the price and their advantage would no longer exist. would resist offering a high price because fewer buyers would purchase from that firm should choose to cooperate with other sellers in...

Question 3: Exact Differential Equation i. Test to see if the following equation is exact, if...

Question 3: Exact Differential Equation i. Test to see if the following equation is exact, if exact solve for the general solution (??/??) +(2? ????+?^3?^?)/(?^2cos?+3?^2?^?)=0 ii. Solve (?+????)??+(?????−2?)??=0 iii. Solve (?^2+?)??+(?^?−?)??=0 iv. (2?−3?)??+(2?−3?)??=0 I am sorry I could not send a photo. Whenever I try from the app it posts another question on the same page. I tried doing them individually and the only thing that happened was that the same question got posted 4 times. I would appreciate your...

Subjects