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

Expert Solution

Colby Messinger answered 2 years ago

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

MUST ANSWER EVERY PART In each of the following situations, Emma is in the exact center...

MUST ANSWER EVERY PART In each of the following situations, Emma is in the exact center of a glass-sided fright 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�s frame of reference, which beam of light travels...

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.

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.

Do a walk-through of the following program segments and determine, in each case, the exact output:...

Do a walk-through of the following program segments and determine, in each case, the exact output: a) int i, j; for (i = 1; i <= 5; i++) { for (j = 1; j <= 5; j++) cout << setw (3) << i; cout << endl; } b) int i, j; for (i = 1; i <= 5; i++) { for (j = (i + 1; j <= 5; j++) cout << setw(5) << j; cout << endl; c) int...

Question