Solve the given differential equation by finding, as in Example 4 from Section 2.4, an appropriate integrating factor. y(6x + y + 6) dx + (6x + 2y) dy = 0

          Solve the given differential equation by finding, as in Example 4 from Section 2.4, an appropriate integrating factor.
y(6x + y + 6) dx + (6x + 2y) dy = 0

Added by Ronald D.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Adi S

07/24/2023

Step 1

First, we rewrite the given differential equation: $$y(6x - y + 6) \frac{dx}{dy} + (6x + 2y) = 0$$ Now, we can rewrite this as a first-order linear differential equation: $$\frac{dx}{dy} + \frac{1}{y}(6x - y + 6) = -\frac{6x + 2y}{y}$$ The integrating factor is Show more…

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