# Boundary Value Problems/Lesson 6

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### 1D Wave Equation

editDerivation of the wave equation using string model.

### General form for boundary conditions.

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### Wave equation with Dirichlet Homogeneous Boundary conditions.

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In the homogeneous problem
with ,

### Finding a solution: u(x,t)

editLet

then substitute this into the PDE.

Where is a constant that can be positive, zero or negative. We need to check each case for a solution.

## Wave Equation with nonhomogeneous Dirichlet Boundary Conditions

editIn the homogeneous problem

## Wave Equation with resistive damping

editIn the homogeneous problem