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xartaan

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

  • one year ago
  • one year ago

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  1. xartaan
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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.

    • one year ago
  2. hartnn
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    try to isolate y

    • one year ago
  3. hartnn
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    if ln a= b then a=e^b

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

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

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

    • one year ago
  7. xartaan
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    c=-ln(8) ?

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

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

    • one year ago
  10. xartaan
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    ahhhh yes I see that

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

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

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

    • one year ago
  14. hartnn
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    welcome ^_^

    • one year ago
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