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Solve the differential equation with the appropriate method. Finalize answer free of fractions, logarithms, and express final answer equated to C.                                                                                                                                                  (2x - 5y + 3)dx - (2x + 4y - 6)dy = 0

Solve the differential equation with the appropriate method. Finalize answer free of fractions, logarithms, and express final answer equated to C.                                                                                                                                                  (2x - 5y + 3)dx - (2x + 4y - 6)dy = 0

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Solve the differential equation with the appropriate method. Finalize answer free of fractions, logarithms, and express final answer equated to C.                                                                                                                                                  (2x - 5y + 3)dx - (2x + 4y - 6)dy = 0

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Hello, may I ask how was this part obtained? Why are there A and B? This part wasn't on our lesson so I was confused. Thank you so much in advance.

Now (4 v+2) A (4v -1) (V+2) ¯ (4v-1) + (v+2) (Av-1) = A (v+2) + B (4v - 4) = v (A + 46) + (2A -B) 4 v +2 4V + 2 Compaxing coefficients both Side e,we get on A + 4B =4 and 2A = 2 and then adding O80 Multiplying j we. get by 4 A + 4B 8A - 4B =8 9A = 12 12 6. 4 Now, Prom O for A = 3 we get + 4B =4 B 2 ニ 50, (4v + 2) 4. 2 (Av-1) (v+2) 3(4v-1) 3 (v+2) Av+2) (Av-1)() 4 dv 2 = AP (1v-1) (av+2) 4 ; J लv-) 2 dv = ^P Av-1)(V42) (4v +2) dv (Av-1) (V+2) 4.1 In (Av-) + o (v+ 2) (4v+2) (Av-1) (v+2) dv = a(4v-1)+응 h(v+)
Transcribed Image Text:Now (4 v+2) A (4v -1) (V+2) ¯ (4v-1) + (v+2) (Av-1) = A (v+2) + B (4v - 4) = v (A + 46) + (2A -B) 4 v +2 4V + 2 Compaxing coefficients both Side e,we get on A + 4B =4 and 2A = 2 and then adding O80 Multiplying j we. get by 4 A + 4B 8A - 4B =8 9A = 12 12 6. 4 Now, Prom O for A = 3 we get + 4B =4 B 2 ニ 50, (4v + 2) 4. 2 (Av-1) (v+2) 3(4v-1) 3 (v+2) Av+2) (Av-1)() 4 dv 2 = AP (1v-1) (av+2) 4 ; J लv-) 2 dv = ^P Av-1)(V42) (4v +2) dv (Av-1) (V+2) 4.1 In (Av-) + o (v+ 2) (4v+2) (Av-1) (v+2) dv = a(4v-1)+응 h(v+)
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