The forum discussion focuses on solving the separable differential equation given by 4xydx + (x² + 1)dy = 0. The solution process involves separating variables, leading to the integral ∫dy/y = ∫-(4xdx)/(x² + 1). The final result is expressed as ln|y| = -2ln|x² + 1| + C, with a substitution of u = x² + 1 utilized in the integration step. Participants emphasize the importance of solving for y explicitly and verifying the solution against the original differential equation.
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Do you have a question?Dusty912 said:Homework Statement
Solve each of the following differential equations:
4xydx + (x2 +1)dy=0Homework Equations
None
The Attempt at a Solution
4xydx + (x2 +1)dy=0
(x2 +1)dy=-4xydx
dy/y=-(4xdx)/(x2 +1)
∫dy/y=∫-(4xdx)/(x2 +1)
ln|y|=-2ln|x2+1| +C
used u-sub on last step fo u=x2 +1