- #1

JJBladester

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## Homework Statement

Solve the following differential equation by using substitution.

## Homework Equations

(x + 2y - 1)dx + (2x + 4y - 3)dy = 0

Let u = x + 2y

## The Attempt at a Solution

u = x + 2y

du/dx = 1 + 2(dy/dx)

(x + 2y - 1)dx + (2x + 4y - 3)dy = 0

(u - 1)dx + (2u - 3)dy = 0

The solution the teacher gave is as follows but I didn't know how to go from my line above to the answer below. I believe it has something to do with getting the dx and dy out of the new equation involving u and then rearranging to solve by separation variables.

K = x + (x + 2y)

^{2}- 3(x + 2y)