Word Count : 418

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We are asked to solve the differential equation: $$ \frac{dy}{dx} = -\frac{2x + y + 1}{4x + 2y - 1}. $$ Step 1: Rewrite the equation in standard form. $$ (4x + 2y - 1) \frac{dy}{dx} + (2x + y + 1) = 0 $$ Step 2: Check if it can be reduced to a homogeneous or linear form. Notice the constants complicate it, so try a substitution: let $$ u = 2x + y $$ so that $$ \frac{du}{dx} = 2 + ______ ___ _______ ________ _______ _________ _________ _____.
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