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Math Help - Need a clarification of a differential equation solution

  1. #1
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    Unhappy Need a clarification of a differential equation solution

    Hello, so as the title says, i have a differential equation, and i already have a solution with steps. However, I dont really know whats going on in the steps or why do they do what they do in the steps. I know this sounds messy so Im just going to show you.
    Need a clarification of a differential equation solution-priklad_bma.png
    From step 3 im lost. Please can someone clarify whats going on with the substitution and why do they use it ?

    Thanks alot.
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  2. #2
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    Re: Need a clarification of a differential equation solution

    The equation is first order linear, so they multiply both sides by an integrating factor so that the LHS can be written as the derivative of a product. Then the solution can be found by integrating.
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