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Problem #4 (20 points) - A Heat-Like Equation Solve for $u(x, t)$ in the region $R = \{(x,t)|0 \le x \le 1,0 \le t\}$ given the partial differential equation, $x^2 \frac{\partial^2 u(x,t)}{\partial x^2} + x \frac{\partial u(x,t)}{\partial x} - 4u(x,t) = x^2 \frac{\partial u(x,t)}{\partial t}$, the boundary conditions: $u(0,t) = \text{finite}$ , $u(1,t) = 1$ and the initial condition, $u(x, 0) = x^2 + 1$. Note that you need not evaluate the integrals in the dot product in your final solution.

          Problem #4 (20 points) - A Heat-Like Equation
Solve for $u(x, t)$ in the region
$R = \{(x,t)|0 \le x \le 1,0 \le t\}$
given the partial differential equation,
$x^2 \frac{\partial^2 u(x,t)}{\partial x^2} + x \frac{\partial u(x,t)}{\partial x} - 4u(x,t) = x^2 \frac{\partial u(x,t)}{\partial t}$,
the boundary conditions:
$u(0,t) = \text{finite}$ ,  $u(1,t) = 1$
and the initial condition,
$u(x, 0) = x^2 + 1$.
Note that you need not evaluate the integrals in the dot product in your final solution.

$Problem #4 (20 points) - A Heat-Like Equation Solve for u(x, t) in the region R = {(x,t)|0 ≤ x ≤ 1,0 ≤ t} given the partial differential equation, x^2 (∂^2 u(x,t))/(∂ x^2) + x (∂ u(x,t))/(∂ x) - 4u(x,t) = x^2 (∂ u(x,t))/(∂ t), the boundary conditions: u(0,t) = finite , u(1,t) = 1 and the initial condition, u(x, 0) = x^2 + 1. Note that you need not evaluate the integrals in the dot product in your final solution.$

Added by Stanley W.

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