Solve using seperation of variables

[Danzilla14]

Hello everyone how yall durrin!
Solve the following DEs by separation 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

 

[timthereaper]

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.

 

[Danzilla14]

Thank you very much kind sir!

 

[timthereaper]

You're welcome. Welcome to PF, by the way.