Math Problem Statement
tut + xux = −2u, x ∈ R, t> 1; u(x, 1) = f(x), x ∈ R.
Solution
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Math Problem Analysis
Mathematical Concepts
Partial Differential Equations
Method of Characteristics
First-order Linear PDE
Formulas
t u_t + x u_x = -2u
Characteristic equation system: dt/t = dx/x = du/(-2u)
General solution: u(x, t) = (1/t^2) * f(x/t)
Theorems
Method of Characteristics
Separation of Variables for First-order PDEs
Suitable Grade Level
Undergraduate (Advanced calculus or introductory PDE courses)
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