Solve using seperation of variables

Danzilla14
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Hello everyone how yall durrin!
Solve the following DEs by Seperation of Variables
eliminate natural logarithms and leave your final answer in implicit form

(3x+8)(y^2 +4)dx - 4y(x^2+5x+6)dy=0
by separation of variables i get
(3x+8)dx/(x^2+5x+6)=4ydy/(y^2 +4)
now I am having trouble integrating the left side of the equation, and on the right side i get 2ln|Y^2 +4|
help me pleeeeeease..
preciate it
 
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Factor and then use method of partial fractions.

\frac{3x+8}{x^2+5x+6} = \frac{A}{x+2} + \frac{B}{x+3}

Take it from there.
 
Thank you very much kind sir!
 
You're welcome. Welcome to PF, by the way.
 

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