Use the indicated method of solution to determine a one-parameter family of solutions for each DE. Note: Primes denote derivative with respect to x. 1. Solve the Bernoulli equation: xy' = 6y + 12x¹y²/3 2. Solve the following differential equation using exact equation and DE with homogeneous coeffi- cients. No need to show test for exactness or to verify that the coefficients are homogeneous. dy dx 3x² + 2y² 4xy 3. Solve (x-y+5)dx+ (2x+y-2)dy = 0. Show solution for the coordinates of point of intersection of the coefficients linear in two variables.
Use the indicated method of solution to determine a one-parameter family of solutions for each DE. Note: Primes denote derivative with respect to x. 1. Solve the Bernoulli equation: xy' = 6y + 12x¹y²/3 2. Solve the following differential equation using exact equation and DE with homogeneous coeffi- cients. No need to show test for exactness or to verify that the coefficients are homogeneous. dy dx 3x² + 2y² 4xy 3. Solve (x-y+5)dx+ (2x+y-2)dy = 0. Show solution for the coordinates of point of intersection of the coefficients linear in two variables.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:Use the indicated method of solution to determine a one-parameter family of solutions for each DE.
Note: Primes denote derivative with respect to x.
1. Solve the Bernoulli equation: xy' = 6y + 12x¹y²/3
2. Solve the following differential equation using exact equation and DE with homogeneous coeffi-
cients. No need to show test for exactness or to verify that the coefficients are homogeneous.
dy
dx
3x² + 2y²
4xy
3. Solve (x-y+5)dx+ (2x+y−2)dy = 0. Show solution for the coordinates of point of intersection
of the coefficients linear in two variables.
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