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gerryliyana

  • 2 years ago

solve y dx + (3xy - 1) dy = 0

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  1. artix_17
    • 2 years ago
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    solve for y or dy/dx?

  2. gerryliyana
    • 2 years ago
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    solve for y :)

  3. gerryliyana
    • 2 years ago
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    \[y dx + (3xy - 1 ) dy = 0\] \[y dx + 3xy dy - dy = 0\]\[y \frac{ dx }{ dy }+3xy - 1 = 0\] \[\frac{ dx }{ dy }+ 3x = \frac{ 1 }{ y }\] 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
    • 2 years ago
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    is it correct??

  5. gerryliyana
    • 2 years ago
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    I got \[xe^{3y} - \int\limits \frac{ e^{3y} }{ y } = C\] for the solution.

  6. Kira_Yamato
    • 2 years ago
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    I'm not too sure, sorry.... But I think it should be ok...

  7. gerryliyana
    • 2 years ago
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    Ok, np @Kira_Yamato i'm not sure for: \[\int\limits \frac{ e^{3y} }{ y } dy\] what results did you get?

  8. Kira_Yamato
    • 2 years ago
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    This is what MatLab gave me

  9. gerryliyana
    • 2 years ago
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    can i see ur script on matlab??

  10. gerryliyana
    • 2 years ago
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  11. Kira_Yamato
    • 2 years ago
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    Sorry I mean Wolfram Alpha

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  12. gerryliyana
    • 2 years ago
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    ok.., thank u Kira :)

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