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2 examples of the method of characteristics for solving PDEs

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1. Use the method of characteristics to solve the advection equation

du/dt=-kdu/dx-ru

subject to the initial condition u(x,0)=f(x).

2. Use the method of characteristics to solve du/dt+te^(-t^2))du/dx=usin(t) subject to the initial condition u(x,0)=e^(-x^2))

(See attachment for the above questions formatted with correct mathematical notation).

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