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Math Help - please help me because tomorrow I will have an exam:(

  1. #1
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    please help me because tomorrow I will have an exam:(

    We found our midterm questions.Please help me to solve them.Thank you so much:

    1)y.y'' + 3(y')^2=0 this is differential equation.find the solution.???


    2)x'=q - 12 + 3x - x^3 q is a bifurcation point.Draw the bifurcation diagram

    3)a)show that any linear 1st order dif. eq. can be writen as a total differential?
    b)obtain 'that' total dif ?

    thank you so much.....again
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  2. #2
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    Quote Originally Posted by berkanatci View Post
    We found our midterm questions.Please help me to solve them.Thank you so much:

    1)y.y'' + 3(y')^2=0 this is differential equation.find the solution.???
    You can write,
    y\cdot y'' = -3y' \cdot y'
    Assuming y does not vanish on (-\infty,\infty):
    \frac{y''}{y'} = \frac{-3y'}{y}.
    Thus,
    \int \frac{y''}{y'} dx = \frac{-3y'}{y} dx + C.
    That means,
    \ln |y'| = -3\ln |y| + C
    Thus,
    \ln |y'| = \ln |y|^{1/3} + C
    Thus,
    \ln |y'| - \ln |y|^{1/3} = C
    Thus,
    \ln \left| \frac{y'}{y^{1/3}}\right| = C \implies \frac{y'}{y^{1/3}} = C \mbox{ where }C\not = 0.
    Now this is a basic equation which is seperable.
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  3. #3
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    thank you so much man.maybe you will survive in my life....because it is exam question....thank you again
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