2. [-/3 Points] DETAILS ZILLENGMATH6 13.3.002. du at 0<x<L, t> 0 subject to the given conditions....
— дt ! [points=4] Q4. Solve the heat equation subject to the given conditions: д?u ди 0<х «п, t> о дх2 ди ди - (0,t) = 0, - (п,t) = 0, t>0 дх дх и(x,0) = п - 3x
au du atua = 90, дх with the initial conditions at t = 0: u=0 if u=-1-1 u=1 - << -1, if -1 <I<0, if 0 < I< 0. (Define u(r, t), x,t and the constant qo appropriately.) (b) Use the method of characteristics along suitable curves r(t) to obtain the implicit equation satisfied by the general solution ur,t) of the PDE given in the first problem (do not have to use the initial conditions at this stage, so there...
(1 point) This problem is concerned with using Laplace transforms to solve PDEs. Given du ди -(x, t) + x -(x, t) = x, x > 0, t> 0 дt дх u(0,t) = 0 t > 0, u(x,0) = 0, x > 0. Find the Laplace transform of u(x, t) which we denote by U(x, s) U(x, s) The find the solution u(x, t) (Note that your answer may require the Heaviside function, i.e., unit step function. In webwork this...
value: 10.00 points For the network shown in the given figure, find v(t) for t> 0. Assume L = 0.9 H. 592 692 20 V 2 A 1292 > 200 + v L The voltage v(t) = V for t>0. Hints References eBook & Resources Hint #1 Hint #2 Hint #3 Hint #4 Check my work
1. Solve the following IBVPs for a string of unit length, subject to the given conditions 100, t) = 0, u(1,t)-0, t>0 a) b) a(x, 0) = f(x), ut (x,0) = g(x) 0 < x < 1 f(x) = sinocoso, g(x) = 0, c = 1/л. f(x) = sinx + (1/2)sin3m + 3sin7m, g(x) = snLTX, C = 1 0, if 0sxs 30( 3 30
[points=4] Q4. Solve the heat equation subject to the given conditions: д?u ди О<x<п, to дх? at' ди ди - (0,t) = 0, - (п,t) = 0, t>0 дх дх u(x,0) = п-х Paragraph В І := =
r Extra Credit: Write a complete analysis of the wave equation with friction for a string of length L subject to initial conditions u(x, 0)-f(x) and (x,0) (t) r Extra Credit: Write a complete analysis of the wave equation with friction for a string of length L subject to initial conditions u(x, 0)-f(x) and (x,0) (t)
5. 0/2 points | Previous Answers ZillEngMath6 10.4.010. Solve the given initial-value problem. x'-(1 -1 X(o) 0 8 eBook Submit Answer Save Progress Practice Another Version
PDE: Ut = Uxx, -00 < x < 0, t> 0 IC: u(x,0) = 38(x) + 28(x – 6) where is the Dirac delta function (impulse). u(x, t) =
please show work i will rate you Extra Credit: Write a complete analysis of the wave equation with friction for a string of length L subject to initial conditions u(x,0) = f(x) and 쓿(x,0) = g(t). Extra Credit: Write a complete analysis of the wave equation with friction for a string of length L subject to initial conditions u(x,0) = f(x) and 쓿(x,0) = g(t).