Solve 4xy dx + (x² + 1) dy = 0

[Dusty912]

Homework Statement

Solve each of the following differential equations:
4xydx + (x² +1)dy=0

Homework 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

 

[Mark44]

Homework Statement

Solve each of the following differential equations:
4xydx + (x² +1)dy=0

Homework 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

Do you have a question?
Your work looks fine to me, but you need to take it one step further and solve for y as a function of x.

After that, check your solution by verifying that it satisifies the original DE.