Solve the following problem: [frac{d^{2} c}{d x^{2}}-P e frac{d c}{d x}=0] Use the boundary conditions (c(0)=1) and (c(1)=0). Solve both for large Pclet number, (P

Solve the following problem:

\[\frac{d^{2} c}{d x^{2}}-P e \frac{d c}{d x}=0\]

Use the boundary conditions \(c(0)=1\) and \(c(1)=0\).

Solve both for large Péclet number, \(P e\), where this is a singular perturbation problem, and for small \(P e\), where this is a regular perturbation problem. Compare your answers with the analytical and numerical solutions. Where is the boundary layer for large \(P e\) ? Is it at \(x=0\) or at \(x=1\) ?