## gerryliyana 2 years ago solve y dx + (3xy - 1) dy = 0

1. artix_17

solve for y or dy/dx?

2. gerryliyana

solve for y :)

3. gerryliyana

$y dx + (3xy - 1 ) dy = 0$ $y dx + 3xy dy - dy = 0$$y \frac{ dx }{ dy }+3xy - 1 = 0$ $\frac{ dx }{ dy }+ 3x = \frac{ 1 }{ y }$ I think, in order to satisfy the equation $$\frac{ dx }{ dy } + p(y)x = g(y) x$$ $$p(y) = 3$$ and $$g(y) = \frac{ 1 }{ y }$$ $\mu(y) = \exp(\int\limits\limits_{0}^{y} p(y) dy) = \exp (\int\limits\limits_{0}^{y} 3 dy) = e^{3y}$ $x = \frac{ 1 }{ \mu(y) }\int\limits_{0}^{y} \mu(y) g(y) dy$ $x = \frac{ 1 }{ e^{3y} } \int\limits_{0}^{y} e^{3y} \frac{ 1 }{ y } dy$

4. gerryliyana

is it correct??

5. gerryliyana

I got $xe^{3y} - \int\limits \frac{ e^{3y} }{ y } = C$ for the solution.

6. Kira_Yamato

I'm not too sure, sorry.... But I think it should be ok...

7. gerryliyana

Ok, np @Kira_Yamato i'm not sure for: $\int\limits \frac{ e^{3y} }{ y } dy$ what results did you get?

8. Kira_Yamato

This is what MatLab gave me

9. gerryliyana

can i see ur script on matlab??

10. gerryliyana

11. Kira_Yamato

Sorry I mean Wolfram Alpha

12. gerryliyana

ok.., thank u Kira :)