- #1

Knissp

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## Homework Statement

dy/dx = (2x + y - 1)^2

## Homework Equations

## The Attempt at a Solution

Let u = 2x + y

du = 2 + dy/dx

dy/dx = du/dx - 2

dy/dx = (2x + y - 1)^2

so du/dx - 2 = (u-1)^2

du/dx = (u-1)^2 + 2

du / ((u-1)^2 + 2) = dx

1/sqrt(2) * arctan ((u-1)/sqrt(2)) = x + c

1/sqrt(2) * arctan ((2x + y -1)/sqrt(2)) = x + c

y = sqrt(2) * tan(sqrt(2) * x + C) + 1 - 2x

BUT the answer in the back of the textbook is y^2 = x^2 + cx^3. Did I mess up or is it a typo? Thank you.