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xartaan

  • 2 years ago

Find the solution to the differential equation \[\frac{ dy }{ dx }+\frac{ y }{ 5 }=0 \] with the initial condition y(0)=8

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  1. xartaan
    • 2 years ago
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    So, ive done separation of variables, and integrated dy/(-y) amd dx/5 and gotten -ln(y) = x/5+C, but I am not sure what to do next.

  2. hartnn
    • 2 years ago
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    try to isolate y

  3. hartnn
    • 2 years ago
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    if ln a= b then a=e^b

  4. RyanL.
    • 2 years ago
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    when x=0 y=8 plug that solve for c and yeah isolate y

  5. xartaan
    • 2 years ago
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    ok, so \[-\ln(y)=\frac{ x }{ 5 }+C\] becomes \[-y=e^(\frac{ x }{ 5 }+C)\]

  6. xartaan
    • 2 years ago
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    so -8=e^(0+c), -8=e^c?

  7. xartaan
    • 2 years ago
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    c=-ln(8) ?

  8. hartnn
    • 2 years ago
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    yup, c=-ln 8 so -ln y +ln 8 = x/5 ln (y/8) = -x/5 got this ?

  9. hartnn
    • 2 years ago
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    property of log, log A-log B =log (A/B)

  10. xartaan
    • 2 years ago
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    ahhhh yes I see that

  11. xartaan
    • 2 years ago
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    y=8*e^(x/5)

  12. hartnn
    • 2 years ago
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    y=8*e^(-x/5)

  13. xartaan
    • 2 years ago
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    Haha yes, making every mistake posssible on this one. Thanks for the help!

  14. hartnn
    • 2 years ago
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    welcome ^_^

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