Question

Need help with how to separate the following differential as have to solve by separation of variables.

Answer 1

Factor
\[\frac{dy}{dx} = \frac{x(y+3) - (y+3)}{x(y-2)+4(y-2)} = \frac{(x-1)(y+3)}{(x+4)(y-2)}\]
Rearrange, separate variables
\[\frac{y-2}{y+3} dy = \frac{x-1}{x+4} dx\]
Proceed with integrating both sides...

Answer 2

Thank you so much! I don't know why I didn't even think of that. I must be running low on energy. I knew I should have had some coffee before doing this! Anyway, thank you again.

Answer 3

yw

Answer 4

\[\frac{ y+3-5 }{ y+3 }dy=\frac{ x+4-5 }{ x+4 }dx\]
\[\left( 1-\frac{ 5 }{ y+3 } \right)dy=\left( 1-\frac{ 5 }{ x+4 } \right)dx\]
integrating both sides
\[y-5 \ln \left( y+3 \right)=x-5 \ln (x+4)+c\]
simplify further.