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Easy Second Order DE question (FP2)

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    Hey guys i'm having a bit of trouble knowing what to do for part a of question 2? (Finding the value of K for 2 marks) Cheers!

    do you find dx/dt etc and plug it back in?
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    (Original post by iMacJack)

    Hey guys i'm having a bit of trouble knowing what to do for part a of question 2? (Finding the value of K for 2 marks) Cheers!

    do you find dx/dt etc and plug it back in?
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    Use the differentials of x with respect to t and plug them into the equation, then solve for k.
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    (Original post by iMacJack)
    Name:  ImageUploadedByStudent Room1474400246.417102.jpg
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    Hey guys i'm having a bit of trouble knowing what to do for part a of question 2? (Finding the value of K for 2 marks) Cheers!

    do you find dx/dt etc and plug it back in?
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    Find the derivatives, substitute into the equation and compare coefficients.
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    you need to find dx/dt and also d2x/dt2 and put them into the LHS... it has to equal the RHS.
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    okay thanks guys I've done this and I come away with dx/dr = -tke^-t and d2x/dt2 = t^2ke^-t

    I plug these in and I don't get anything seemably solvable?


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    (Original post by iMacJack)
    okay thanks guys I've done this and I come away with dx/dr = -tke^-t and d2x/dt2 = t^2ke^-t

    I plug these in and I don't get anything seemably solvable?


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    Er, you got them wrong. \frac{d}{dt}(ke^{-t})=-ke^{-t} \not= -tke^{-t}
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    (Original post by RDKGames)
    Er, you got them wrong. \frac{d}{dt}(ke^{-t})=-ke^{-t} \not= -tke^{-t}
    Back to the basics then!! how is that the case? (Apologies we have been thrown into FP2 without doing C3/4 so I'm having to pick up all the differentiation rules as I go)


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    (Original post by iMacJack)
    Back to the basics then!! how is that the case? (Apologies we have been thrown into FP2 without doing C3/4 so I'm having to pick up all the differentiation rules as I go)


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    Chain rule. (and maybe product rule if you REALLY need it for the differential with k)

    y=ke^{-t}

    Let u=-t \Rightarrow \frac{du}{dt}=-1

    \Rightarrow y=ke^u \longrightarrow \frac{dy}{du}=ke^u

    \frac{dy}{dt}=\frac{dy}{du} \cdot \frac{du}{dt} = ke^u \cdot -1 = -ke^{-t}
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    (Original post by iMacJack)
    Back to the basics then!! how is that the case? (Apologies we have been thrown into FP2 without doing C3/4 so I'm having to pick up all the differentiation rules as I go)


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    Do diff and integration in C3-4 to the tea before doing FP2. Your gna mislearn stuff and damage your foundation in calculus otherwise.


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    (Original post by physicsmaths)
    Do diff and integration in C3-4 to the tea before doing FP2. Your gna mislearn stuff and damage your foundation in calculus otherwise.


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    agreed
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    (Original post by physicsmaths)
    Do diff and integration in C3-4 to the tea before doing FP2. Your gna mislearn stuff and damage your foundation in calculus otherwise.


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    I don't have a choice - our school is making us do it this way! only other way would be to learn the calculus off my own back which I'd need to allocate time for which I don't really have right now


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    Can someone do this and tell me what they get by the way please? I get 5/3 and I don't have the solution! (value of K)


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    (Original post by iMacJack)
    Can someone do this and tell me what they get by the way please? I get 5/3 and I don't have the solution! (value of K)


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    Yes, that's right.
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    (Original post by NotNotBatman)
    Yes, that's right.
    Awesome thank you, also I might be wrong but for the second part I got A = -5/12 and B = -1/4, then plugged that back into the comp function and particular integral to get x = -5/12 e^7t - 1/4 e^-3t + 5/3 e^-t


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    (Original post by iMacJack)
    I don't have a choice - our school is making us do it this way! only other way would be to learn the calculus off my own back which I'd need to allocate time for which I don't really have right now


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    At the very least you NEED to learn the chain rule, product rule, quotient rule, integration by substitution, and integration by parts. Take a look at pages 24-29 (or pages 22-27 if you look at the numbers written at the bottom of the pages) of http://www.physicsandmathstutor.com/...C3%20Notes.pdf, and at pages 12-21 (or 10-19 if using the numbers at the bottom of the pages) of http://www.physicsandmathstutor.com/...C4%20Notes.pdf
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    (Original post by HapaxOromenon3)
    At the very least you NEED to learn the chain rule, product rule, quotient rule, integration by substitution, and integration by parts. Take a look at pages 24-29 (or pages 22-27 if you look at the numbers written at the bottom of the pages) of http://www.physicsandmathstutor.com/...C3%20Notes.pdf, and at pages 12-21 (or 10-19 if using the numbers at the bottom of the pages) of http://www.physicsandmathstutor.com/...C4%20Notes.pdf
    Awesome I'll get working on that, cheers


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    (Original post by iMacJack)
    Awesome thank you, also I might be wrong but for the second part I got A = -5/12 and B = -1/4, then plugged that back into the comp function and particular integral to get x = -5/12 e^7t - 1/4 e^-3t + 5/3 e^-t


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    Incorrect, I think. Your CF should be Ae^{-4t}+Be^{-3t} so I do not know where you pulled an e^{7t} from?
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    (Original post by iMacJack)
    Awesome thank you, also I might be wrong but for the second part I got A = -5/12 and B = -1/4, then plugged that back into the comp function and particular integral to get x = -5/12 e^7t - 1/4 e^-3t + 5/3 e^-t


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    That's not what I got, the power of 7t seems wrong.

    (Original post by iMacJack)
    Awesome I'll get working on that, cheers


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    If you haven't done all of the differentiation and integration chapters, don't start on second order differential equations yet, solidify your knowledge on the necessary core stuff first.
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    (Original post by NotNotBatman)
    That's not what I got, the power of 7t seems wrong.



    If you haven't done all of the differentiation and integration chapters, then don't start on second order differential equations yet, solidify your knowledge on the necessary core stuff first.
    Yeah I didn't mean 7t! & we have gone over all the chain rule, product rule etc quickly, I get it, I just need to put it into practice a few more times get fully comfortable with it! Thanks, I was able to do the rest of the worksheet relatively easily!


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    (Original post by iMacJack)
    Awesome I'll get working on that, cheers


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    For second order DEs, you need to know the differentiation from C3/4 but not the integration. You'll need that for first oder ones though.

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