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Math Help - General solution to differential equation

  1. #1
    jsl
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    General solution to differential equation

    Hi! I'm having trouble with this problem on my homework. Any help you can give would be wonderful!! Thanks!


    Consider the differential equation:
    .
    a) Find the general solution to the above differential equation. (Instruction: Write the answer in a form such that its numerator is 1 and its integration constant is --- rename your constant if necessary.)

    b) Find the particular solution of the above differential equation that satisfies the condition at .
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  2. #2
    MHF Contributor Drexel28's Avatar
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    Quote Originally Posted by jsl View Post
    Hi! I'm having trouble with this problem on my homework. Any help you can give would be wonderful!! Thanks!


    Consider the differential equation:
    .
    a) Find the general solution to the above differential equation. (Instruction: Write the answer in a form such that its numerator is 1 and its integration constant is --- rename your constant if necessary.)

    b) Find the particular solution of the above differential equation that satisfies the condition at .
    I am just going to rewrite this as

    y'=y^2\left(x^3-x\right) if you don't mind.

    Then \frac{y'}{y^2}=x^3-x So

    \int\frac{y'}{y^2}dx=\int\left[x^3-x\right]dx. Evaluating gives

    \frac{-1}{y}=\frac{x^4}{4}-\frac{x^2}{2}+C

    Solving gives y=\frac{-4}{x^4+2x^2+C_1}
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  3. #3
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    actually:

    (a) 4/(t^4-2t^2+4C)
    (b) 4/(t^4-2t^2+1)
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