Asked by Anonymous
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.
dy/dx = (2x+1) / (y+1)? I keep messing it up.
Answers
Answered by
MathMate
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
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
Answered by
Anonymous
Thank you! How would I isolate y by itself to make this a y= expression?
Answered by
MathMate
This would be more messy if you are looking for an <i>explicit</i> 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.
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.