please and thank you 1. Solve V2u= 0 over 0Sx<L and 0sysH subject to (1) 10%...
5. Solve IBVP 11(0,1)-α, u(L,t)-β u(x,0)- f(x) 120 0Sx SL b) u-100, β-100, f(x)-50x( l-x), L-1, c-1.
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9. (10 pts) Solve the following equation subject to the condition y(0) dy_2x + 2x 10. (10 pts) Find the general solution of the differential equation below. y *(1-x)
ou(x.y)@uxy)o for the temperature 2. Solve Laplace's equation distribution in a rectangular plate 0sx s1, 0sysl subject to the following conditions. (a) u(0,y)-0, uy)-0, u(x,0)-fx), u(x,I)-0 au (x,y) x, y y- o
ou(x.y)@uxy)o for the temperature 2. Solve Laplace's equation distribution in a rectangular plate 0sx s1, 0sysl subject to the following conditions. (a) u(0,y)-0, uy)-0, u(x,0)-fx), u(x,I)-0 au (x,y) x, y y- o
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3. Suppose that an object moves along the helix r(t) - (2 cos t, 2 sin t, L.) , 2π subject to the force field F-(-y, x, z). Determine the work 0-t done.
3. Suppose that an object moves along the helix r(t) - (2 cos t, 2 sin t, L.) , 2π subject to the force field F-(-y, x, z). Determine the work 0-t done.
please
solve #2
Solve the following problems subject to the given boundary conditions. Show the formulas for any arbitrary constants (Ao, An, Bn), but you do not need to actually calculate them tu a(0. t)=0. u(1, t) = 5 u(z,0-82-1 2 0< x<2, t0 u(0, t) = 0, u(2. t) = 0 a(x, 0) 0, tr(r,0) = 0 3 ー+-=-10, 0
2. We are lo solve y" -ky -) (O < x < L) subject to the boundary conditions y(0)y(L)0. a) Find Green's function by direct construction and show that for x ξ? b) Solve the equation G"- kG -(x - by the Fourier sine series method. is equivalent to the solution Can you show that the series obtained for G(x | found under (a)?
2. We are lo solve y" -ky -) (O
Really short question! Please help me to solve, thank
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(10%)Q3 (Logistic regression): We collected n 15 independent binary observations : i- 1, , 15) and their corresponding covariates {xi : і = 1, , 15). Assume the relationship between yi and zi (for i = 1, , 15) is Vi ~ Bernoulli(p.) and logit(Pi)-α+82i, where logit(t) = log ti. Please 1) write down the likelihood function L(a, B|x, y) of the logistic regression model; 2) derive the Newton method...
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In Problem 27 of Exercises 4.9 you were asked to solve the following linear system dx1 1 dt 50 dx2 1 2 dt 50 75 dx3 1 2 x2 75 dt 25 using elimination techniques. This system is a mathematical model for the number of pounds of salt x(t), x2(t), and x3(t) in the connected mixing tanks A, B, and C shown in Figure 3.3.8 on page 112 (a) Use the eigenvalue method of this section...
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D ie 15 points 50 1. Solve the initial value problem y + 4y' + 40y = cos 3t. y(0) = 0, 7(0) = - 1. 2. Over what interval can you be sure that there is a solution to the initial value problem (tỷ - 36 (t? - 1) / + y =t-. (3) = - 3, 4 (3) = 0 ? Why? 3. Let 41. y2 be solutions to...
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b) Solve the following ODE using the substitution, u = dy (x - y) = y A c) Solve the Bernoulli's ODE dy 1 dx + y = xy2 ; x > 0