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Explain why you cannot find f(x,y) such that ?f(x,y) = ( x2+3xy2, 2xy+y3+1).
Consider the heat equation ?u/?t= k(?2u/?x2) ,0=x=L t>0 .
Find the solution u(x,t) of the heat equation: ut = 1/2 uxx
The bending moment M at position x m from the end of a simply supported beam of length L m carrying a uniformly distributed load of w Kn m-1 .
Solve the following PDE: du/dt = d^2u / dx^2,u(x, 0) = sin^2(x), u(0, t) = 0, u(Pi, t) = 0,
Find the particular solution of the differential equation , (dy/dx) + ycos(x) = 6cos(x) w/ y(0) = 8
y'''-11 y'' + 18 y' = 0 w/ y(0) = 1, y'(0) = 3, y"(0) = 4
Calculate uxx, uyy and uxy and show that uxx and uyy are continuous in the whole disk, but that u?c2. Calculate f := - ?u.
an posses a nontrivial solution which vanishes at x=0 and x=1 only if ? is such that J1/4 (1/2v?)=0,and that corresponding to such a characteristic number ?k.
The population of a community is known to increase at a rate proportional to the number of people present at time t.
The problem that I'm having is that there is a nonconstant factor of (x^2+y^2+z^2)^(-1/2) appearing on the RHS of this equation, making it non-trivial to solve.
Suppose that 0
Use the Secant method to show that sequence below converges to vQ, where Q > 0, given "good" starting values x0 and x_1: xn+1 = (xnxn-1 + Q) / (xn + xn-1).
Suppose that y(x)' : f(x,y(x)) on the interval [x0, x1] with y (x0) = y0.
If you were to transform this PDE with the substitution S = Kex, where x is a variable and K a constant, what would be the resulting equation?
Assuming a drag coefficient of k=1/800 lb m/ft, how high does the arrow go? does your answer depend on the objects mass?
Show that for any constants c and d, |d| < 1, the equation x = c + d cos (x) = g(x) has a unique solution alpha.
Determine the flow Qt : R^2 into R^2 for the nonlinear system: x' =f(x) with f(x) = [ -x1 ]
Find the unique solution (and proof that it is unique) and the maximal interval of the initial value problem x' = x^3, x(0) = xo for any xo E R.
Why not just use Newton's Interpolatory Divided Difference formula to get an nth degree interpolating polynomial?
Solve the two-dimensional wave equation for a quarter-circular membrane, 0
Experiment Variable - is one that is purposefully manipulated by myself, such as taking different routes to work.
Determine the order of each differential equation, and whether or not the given functions are solutions of that equation on some interval of x values.
Evaluate your solution for N(t) as t?8 . For what values of N will N ?=0?
A number is divisible by 2 if the last digit is divisible by 2. A number is divisible by 4 if the last two digits form a number divisible by 4.