• Express y in terms of x for differential equation dy/dx=ylny

(I’m officially out of ideas again)

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    6 months ago
    solution

    Not sure if I’d have gotten this one without Cavy’s hint, I’m pretty bad with differential equations

    Let z = ln(y)

    Then z = dy/dx / y

    dy/dx / y is the derivative of ln(y)

    So we have z = d/dx ln(y), or ln(y) = d/dx ln(y)

    ln(y) is its own derivative - so we must have ln(y) = e^x, which implies y = e^(e^x)