Solve using seperation of variables

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Homework Help Overview

The discussion revolves around solving a differential equation using the method of separation of variables. The original poster presents a specific equation and expresses difficulty in integrating one side of the equation.

Discussion Character

  • Exploratory, Mathematical reasoning, Problem interpretation

Approaches and Questions Raised

  • The original poster attempts to separate the variables and integrate both sides of the equation but encounters challenges with the integration process. Another participant suggests factoring and using partial fractions as a potential approach to simplify the left side of the equation.

Discussion Status

Some guidance has been offered regarding the use of partial fractions, and the original poster has acknowledged this assistance. The discussion appears to be progressing with participants exploring different methods to tackle the integration issue.

Contextual Notes

The original poster requests to eliminate natural logarithms and leave the final answer in implicit form, indicating specific constraints on the solution format.

Danzilla14
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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
 
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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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