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Math Help - nonlinear second order

  1. #1
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    nonlinear second order

    I know we can use the subsittion of m = y' for 1 and 2, then let y'=m(y(t))for 3 and 4, but I have a hard time to solve for the answernonlinear second order-nonlinear.jpg


    as the answers are given, can anyone show me the setps, I need to undertsand this for the test tomorrow

    the question is inside the image and
    tha answers are
    1. C1x^2+C2
    2. C1lnt+C2+t^2
    3. [C1+C2^{e^t}]^{1/2}
    4.  C1 tan(C1t+C2)
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  2. #2
    A Plied Mathematician
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    As you've indicated, reduce the order for 1 and 2. For 3, note that (yy')' = LHS. Then integrate. For 4, just integrate directly once. You'll get a first-order separable equation out of that.
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  3. #3
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    I did that, but for some reason i can't get the right answer, can you show me the steps if possible?
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  4. #4
    A Plied Mathematician
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    can you show me the steps if possible?
    No, but if you show your work, I'll comment on it. Please distinguish the problems and label clearly. Thanks!
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