Recent content by King Tony

Think I figured it out now, derp... I just chose a reference function r(x, t) = r(x) = c_{1}\frac{x^2}{2} and solved for c1 which allowed me to generate a new linear homogeneous PDE and summed up the solution and the reference function to find the final solution. Would be nice if someone...

Homework Statement u_{t} = ku_{xx} u_{x}(0, t) = 0 u_{x}(L, t) = B =/= 0 u(x, 0) = f(x) Homework Equations The Attempt at a Solution I believe that no equilibrium solution exists because we can't solve u_{xx} = 0 with our boundary conditions. I'm a little lost as to where...

It just looks like you need to take the given solution and plug it into the differential equation to "test" if it is true.

You got the first question right except I think you just mis-wrote your final answer that's boxed. It looks like you accidentally moved the x^6 to the bottom when you went to the last step.

Thankyou! I think I'm on the right track, I see how that would make both sides equal only if C is a subset of A.

Homework Statement Let A, B, C be any sets. Prove that if C\subseteq A, then (A\cap B)\cup C = A\cap (B\cup C) Homework Equations ? The Attempt at a Solution Don't even know where to begin, If someone could point me in the right direction, that would be the best.

You're so right, thankyou!

Sorry, took a little while to figure out the symbols and dealies, pretty sure it's good to go right now.

Homework Statement Let S be the region in the first octant under the plane 3x + 2y +z = 4. Find the volume of S. Homework Equations idk? The Attempt at a Solution \int^{\frac{4}{3}}_{0}\int^{\frac{3}{2}x + 2}_{0}\int^{-3x - 2y + 4}_{0}dzdydx =...