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    Solving Partial Differential Equations by Change of Variables and Characteristic Curves

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    In solving this problem, derive the general solution of the given equation by using an appropriate change of variables.

    1. ∂u/∂t - 2 ∂u/∂x = 2

    Answer: u(x,t) = f(x + 2t) - x

    In this exercise, (a) solve the given equation by the method of characteristic curves, and (b) check you answer by plugging it back into the equation.

    2. ∂u/∂x + x2 ∂u/∂y = 0

    Answer: (a) u(x,y) = f(1/3 x3 - y)

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    https://brainmass.com/math/partial-differential-equations/solving-partial-differential-equations-change-variables-162141

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    Solving Partial Differential Equations by Change of Variables and Characteristic Curves is investigated. The solution is detailed and well presented.

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