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Homework Statement Given the initial value problem: \frac{(u)}{(1-e^-(2x))}u_{x}+ \frac{\sqrt{t}}{u}u_{t}=1, with x, t, u > 0 Subject to condition u(x,1)=e^{-x} Homework Equations a) Classify given partial differential equation. b) Write the characteristic equations. By...

There is a typo: shoul be -x instead of one of y \dot{x} = y+(x^2+y^2-3)^2 (x^3-x+xy^2) \dot{y} = -x+(x^2+y^2-3)^2 (y^3-y+x^2y)

Homework Statement The trajectory of an arrow in space obeys the following system of equations: \dot{x} = y+(x^2+y^2-3)^2 (x^3-x+xy^2) \dot{y} = y+(x^2+y^2-3)^2 (y^3-y+x^2y) 1. Questions a) Derive an ODE for the radial coordiante r(t) = \sqrt[]{x^2(t)+y^2(t)} b) Show that the...

Description 1. Prove that operators i(d/dx) and d^2/dx^2 are Hermitian. 2. Operators A and B are defined by: A\psi(x)=\psi(x)+x B\psi(x)=d\psi/dx+2\psi/dx(x) Check if they are linear. The attempt at a solution I noted the proof of the momentum operator '-ih/dx'...

\nabla \cdot \vec{F} = (d/dx, d/dy, d/dz) \cdot (x^2,xy,xz) = 2x+x+x=4x

Homework Statement Let S be a smooth surface enclosing the volume V, and let \vec{n} to be the unit outward normal. Using the Divergence theorem show that: ∫∫ x \vec{r} ° \vec{n} dS = 4 * ∫∫∫ x dV, where \vec{r}=(x,y,z) Homework Equations Divergence theorem...

Homework Statement Hi. I think it will be easiest to understand if I upload a word document as it has some complicated characters. The bold letters stand for vectors. http://www.sendspace.pl/file/1f830d4ff025d966f71b62c Homework Equations Divergence theorem...