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Math Help - Multiple variables in exponent of first order ODE

  1. #1
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    Multiple variables in exponent of first order ODE

    The differential equation is stated as:

    y'=3x exp (x+2y)/y

    I have two questions about this problem. First, I am interpreting this problem as follows:

    y'=3x^[(x+2y)/y]

    Is that correct? If so, that leads me to my second question. Am I able make any substitutions to simply that exponent? It seems as if the substitutions are too complicated thereby making my substituted terms dy and dx extremely complex.

    I am not sure how to proceed.
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  2. #2
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    Re: Multiple variables in exponent of first order ODE

    Quote Originally Posted by cheme View Post
    The differential equation is stated as:

    y'=3x exp (x+2y)/y
    y' = \frac{3x \times e^{x+2y}}{y} = \frac{3x \times e^{x}\times e^{2y}}{y}
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  3. #3
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    Re: Multiple variables in exponent of first order ODE

    Quote Originally Posted by pickslides View Post
    y' = \frac{3x \times e^{x+2y}}{y} = \frac{3x \times e^{x}\times e^{2y}}{y}
    Thank you. That was my issue with this problem.
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