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Math Help - First order differential and linear equations

  1. #1
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    First order differential and linear equations

    Hello guys,

    I need help with two of the most weird equations i have ever seen.

    Problem 1:
    Solve the initial value problem

    xy' + 3y = x^7, y'(0) = 3.

    Problem 2:
    Solve the initial value problem

    (x^2)y' + y = 1, y(1) = 2.


    Thanks, in advance.
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  2. #2
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    Quote Originally Posted by tapiaghector View Post
    Hello guys,

    I need help with two of the most weird equations i have ever seen.

    Problem 1:
    Solve the initial value problem

    xy' + 3y = x^7, y'(0) = 3.

    These quations aren't very weird at all. You need to use the integrating factor method for both. They just need a little re-arranging first.

    xy' + 3y = x^7

    divide both sides by x

     y' + \frac{3}{x}y = x^6

    Then follow the steps in this post

    http://www.mathhelpforum.com/math-he...equations.html
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  3. #3
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    hey thanks my friend, i have another question, how do you evaluate y'(0) = 3?
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  4. #4
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    Quote Originally Posted by tapiaghector View Post
    hey thanks my friend, i have another question, how do you evaluate y'(0) = 3?
    After you've found your general solution you differentiate it. Then you substitute x = 0 and equate the result to 3. Then you solve for your arbitrary constant of integration.
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  5. #5
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    Quote Originally Posted by tapiaghector View Post
    hey thanks my friend, i have another question, how do you evaluate y'(0) = 3?

    This is to be evaluated after you have a general solution.

    What is your general solution?

    I have something along the lines of

    y=\frac{ \int x^6 e^{3ln(x)} dx}{e^{3ln(x)}}

    You will need to apply integration by parts from here.
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