Math Problem Statement
S∂u1/∂t +8∂u2/∂x =0 ∂u2/∂t +∂u1/∂x =0. u1(x,0)=sin. u2(x,0)=x²
Solution
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Math Problem Analysis
Mathematical Concepts
Partial Differential Equations (PDEs)
Wave Equation
Initial Conditions
Formulas
∂u1/∂t + 8∂u2/∂x = 0
∂u2/∂t + ∂u1/∂x = 0
General solution for wave equation: u1(x, t) = f(x - √8 t) + g(x + √8 t)
Theorems
Wave equation
Method of characteristics
Decoupling method for PDEs
Suitable Grade Level
University Level
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