Professor Kate Poirier | OL67 | Fall 2020

WebWork 1 — First Order Linear Help Please

Tried both integrating factors (because of the hint) and variation of parameters and I’m at a dead end. Did anyone approach these questions differently.

Problem 6

Getting the same answer with integrating factor method and variation of parameters

Problem 8


  1. Kate Poirier

    Hi Brian. I can take a closer look at your work later. For now, don’t forget that you can always check your solutions by plugging them into the differential equation, like you did in Section 1.2.

  2. Kate Poirier

    Your work for Problem 6 is *almost* perfect, but there’s a problem with your coefficients. You probably won’t have to re-do the whole solution if you can carefully track your constant multiples in the work you’ve already done.

    • Brian Enriquez

      It was the constants! Thank you

  3. Kate Poirier

    Okay there is a more serious error in your work for Problem 8, but it’s early on so I didn’t check the rest! On the right in yellow you’ve got y_1 = e^{-7 \ln(t)}, which is fine (except don’t forget that \int \frac{dt}{t} = \ln(|t|) + C…you’re missing the absolute value, but this isn’t the real problem). Then you’ve simplified e^{-7 \ln(t)} = -7t and *this* is the part that’s not correct. Certainly, the exponential and logarithmic functions are inverses, so you’ll get some cancellation, but that -7 coefficient kills this vibe. BUT you can use your log rules to rewrite the exponent to get the exponential/logarithmic cancellation you’re hoping for. Hope that helps!

    • Brian Enriquez

      I corrected solving for y_1 and checked if the general solution is valid, but WebWork still won’t accept my answer

      • Kate Poirier

        I’ll look into it.

      • Kate Poirier

        Your answers for #8 are correct. If you remove the absolute value bars from your particular solution, WeBWorK will accept it.

        Your general solution is also correct. I’m digging around in the WeBWorK code to figure out why it’s not accepting your answer, but I don’t see the problem yet. Luckily, you’re the only one who’s impacted by this weird thing. I’ll manually change your score for this question (once I remember how to) and you can move on with your life!

      • Kate Poirier

        Brian, I have an update! I asked the WeBWorK admin for help with the code, and they were able to fix it. So if you re-submit your answer (without absolute values), WeBWorK will accept it now!

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