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Math Help - differential equation with substitution!!!

  1. #1
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    differential equation with substitution!!!

    using the substitution u = y-x solve dy/dx = sin(y-x) after substitution i get sin u but then how do integrate with respect to x????
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  2. #2
    Member Henderson's Avatar
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    First thing to notice is that if u = y - x, then \frac{du}{dx} = \frac{dy}{dx} -1.

    Substituting into your equation, then, will give you:

    \frac{du}{dx} = sin(u) +1.

    Do you see where to take it from here?
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  3. #3
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    i got to the form int (1/(sin u + 1)) du = int dx but how do integrate the part on the left?
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  4. #4
    Math Engineering Student
    Krizalid's Avatar
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    Multiply top and bottom by 1-\sin u.
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  5. #5
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    Quote Originally Posted by Henderson View Post
    First thing to notice is that if u = y - x, then \frac{du}{dx} = \frac{dy}{dx} -1.

    Substituting into your equation, then, will give you:

    \frac{du}{dx} = sin(u) +1.

    Do you see where to take it from here?
    i tried this but shouldn't the correct form be du/dx = sin (u) - 1 and not plus 1 like you wrote, Henderson??
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