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    Equation Set: Solving Differential Equations

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    Please answer the following:

    1. Find the general solution y(x)of the given differential equation

    dy/dx = (sqrt)(y + 1)

    2. Differentiate the following function

    f(x) = x(ln(x))^2

    3. Evaluate the following indefinite integral

    Integral (e^(-1/x^2))/(x^3) dx

    4. Differentiate the following function
    g(t) = tan^-1e^t

    5. Find the limit of the following
    lim (x -> 0) sin(2x)/(x)

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    Solution Summary

    This solution is comprised of a detailed, step by step response in which five different differential equations are solved. The different techniques used for solving the equations, such as the implementation of the product rule for one of the equations, are outlined in each case.