Posted by **Anonymous** on Tuesday, June 5, 2012 at 9:43pm.

Could someone show me the steps to separating the variables in the following differential equation:

dy/dx = (2x+1) / (y+1)? I keep messing it up.

- CALCULUS -
**MathMate**, Tuesday, June 5, 2012 at 10:08pm
To separate:

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

Cross multiply:

(y+1)dy = (2x+1)dx

To solve, integrate both sides

(y^2/2+y) = (x^2+x)+C

where C is an integration constant

- CALCULUS -
**Anonymous**, Tuesday, June 5, 2012 at 10:24pm
Thank you! How would I isolate y by itself to make this a y= expression?

- CALCULUS -
**MathMate**, Tuesday, June 5, 2012 at 11:39pm
This would be more messy if you are looking for an *explicit* solution.

You would solve for y as a quadratic equation, and verify that all solutions obtained from the equation are actual solutions.

Most of the time, an implicit solution (where y occurs in more than one term or embedded as a function) is acceptable.

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