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1. Our Solar System name?

Ok, so I've been passionately researching my latest novel idea as it takes place in an extremely far fetched future with long range interstellar travel and all that and the brink of controlled time modulation etc... While doing this, I've been able to name every site, system, planet of...
2. Rawr! Stuck on ODE (linear 1st order!)

Homework Statement Solve the initial value problem: y'+\frac{4y}{x+8}=(x+8)^{8} , y(0)=8. The differential equation is linear. Homework Equations N/A The Attempt at a Solution I can see that the equation is in the form y' +P(x)*y = Q(x) so I'm like "easy, lemme get an...
3. Improper Integral (Calc II)

Been doing some calculus review to knock the rust off for this coming fall semester and I got stuck... Homework Statement From Stewart's book (Early Transcendentals: 6E): (7.8 pg517 #69) Determine how large the number "a" has to be so that: \int\stackrel{\infty}{a}\frac{1}{x^{2}+1}dx <.001...
4. Building an artificial lake

"Building an artificial lake" Howdy PF :smile: this is actually a Calc III project I'm working on with two others. We are in the beginning stage and are having a little trouble on how to exactly go about doing this problem... Homework Statement "A small man made lake is being proposed on...