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Diff EQ w/ I.C. anyone see where i f'ed it up?

  1. Jan 15, 2006 #1
    Its me again! i'm just having a full day of Diff EQ!! 90% of the time i'm wrong but i'm learning slowly! but here is another problem:
    The directions say: Find the particular solution of the differential equation
    \frac{dy}{dx} + 5 y = 7
    satisfying the initial condition y(0)=0.
    Answer: y = ?

    I submited this answer, and it was wrong:
    (e^x*e^(ln(7^(-1/5)))^-5)/5 - 7/5

    Here is my work:
  2. jcsd
  3. Jan 15, 2006 #2

    Tom Mattson

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    The only mistake I see is that in the next to last step you divided the left side by -5 while dividing the right side by +5. Fix that and your answer should be correct.
  4. Jan 15, 2006 #3
    Thanks tom, but i submitted:
    -(e^x*e^(ln(7^(-1/5)))^-5)/5 +7/5

    and it still said it was wrong :/
  5. Jan 15, 2006 #4


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    [itex] e^C [/itex] is a constant. There is no need to solve for C in the manner you did. Just set [itex] e^C = C_1 = C [/itex] (The last since the name of the constant is immaterial). Now see what you get.
  6. Jan 15, 2006 #5


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    And why in the world are writing such a complicated thing as
    (e^(ln(7^(-1/5)))^(-5)? That's just 1/7.

    Back where you had "(-1/5)ln(-5y+ 7)= x+ C", I would have been inclined to write ln(-5y+ 7)= -5x+ C' (C' = -5C) then -5y+ 7= C"e^(-5x)
    (C"= e^C') and finally y= C"' e^(-5x)- 7/5 (C"'= C/(-5)). (In fact, I would probably have just written C for each of C, C', C", C"' reminding myself that they different values of C.)

    Now, if y(0)= Ce^(-5(0))- 7/5= C- 7/5= 0, then C= 7/5 and
    y(x)= (7/5)(e^(-5x)- 1).

    You said it still said it was wrong. Are you submitting this to an automatic checker? Those things are notoriously hardnosed about the answer being in exactly the right form.
  7. Jan 15, 2006 #6
    your first answer may not have been wrong..if you were using a computerized answering system they may have been looking for the simplest form of the solution...
    -(e^x*e^(ln(7^(-1/5)))^-5)/5 +7/5 simplify that. which you shouhld be able to do.

    interesting that you solved for C before solving for the general why solution =]
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