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Math Help - initial value problem DFQ

  1. #1
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    initial value problem DFQ

    I need to solve this initial value problem:

    sin(x)dy/dx + ycos(x) = xsin(x) with initial condition y(pi/2)=2

    Please help there are NO examples of my book of this type of problem

    THANKS
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  2. #2
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by cheertcc101 View Post
    I need to solve this initial value problem:

    sin(x)dy/dx + ycos(x) = xsin(x) with initial condition y(pi/2)=2

    Please help there are NO examples of my book of this type of problem

    THANKS
    the book has these kinds of problems. it is just that here, the started you midway. does the "integrating factor method" ring a bell?

    hint: note that the left hand side is the derivative of y \sin x (by the product rule)

    now can you continue?
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  3. #3
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    Quote Originally Posted by cheertcc101 View Post
    I need to solve this initial value problem:

    sin(x)dy/dx + ycos(x) = xsin(x) with initial condition y(pi/2)=2

    Please help there are NO examples of my book of this type of problem

    THANKS
    Hint: \sin x \cdot y' + y\cos x = x\sin x \implies ( y\sin x  ) ' = x\sin x
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    Answer??

    Is this the answer?? ..

    y= (-2yln(sinx)-x^2)/2 + 4 - pi^2/4 ????
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  5. #5
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    Quote Originally Posted by Jhevon View Post
    the book has these kinds of problems. it is just that here, the started you midway. does the "integrating factor method" ring a bell?

    hint: note that the left hand side is the derivative of y \sin x (by the product rule)

    now can you continue?


    Is this the answer?? ..

    y= (-2yln(sinx)-x^2)/2 + 4 - pi^2/4 ????
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  6. #6
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by cheertcc101 View Post
    Is this the answer?? ..

    y= (-2yln(sinx)-x^2)/2 + 4 - pi^2/4 ????
    no. where did ln... come from?
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