JO SUUS. 7.12. Solve the BVP y" = -2e-3y + 4(1+x)-3, 0<x<1, subject to y(0) =...
2. Use the Laplace Transform to solve the initial value problem y"-3y'+2y=h(t), y(O)=0, y'(0)=0, where h (t) = { 0,0<t<4 2, t>4
8 Minimize z= x + 3y 9 + 22 54 + 4yΣ Subject to 2y + 2 > ΛΙ ΛΙ ΛΙΛΙ ΛΙ 14 O Σ Ο Minimum is Maximize z = 4x + 2y 32 + 4y < < 32 5x + 5y < Subject to 0 VI VI ALAI y 0 Maximum is
Exercise 9. Solve the BVP a(0, t) = 0 u(r, t)-Uz(n, t) = 0 u(z, 0) = sin z 0<x<π, t>0, t >0 t > 0 (z,0) = 0 2
1. Verify that fxr (x,y) -2e-x-y 0 < x < 00, x < y < is joint probability density function 2. Compute the probability that X < 1.and Y < 2.
1. Solve the following DE: (50 pts) (1, if 0<x51 a) y+ y = f(x), y(0) = 3 where f(x)= 0, if x>1 (10 pts)
A 3) solve 0<-t<1 y'-y=f(t), ft)-(1 , 0, (use La t>=1 y(0)-0. ay-(2e-1)-(e11)u(t-1) b) y-(e-1)-(e1-1)u(t-1) c) y-(e1)-(2e1-1)u(t-1) d) y-(2e'-1)-(2e1-1)u(t-1)
NIS 4) The joint pdf of X and Y is 1, 0<x<1, 0<y< 2x, fx,8(8,y) = { 0, otherwise. otherwise. or 1 (Note: This pdf is positive (having the value 1) on a triangular region in the first quadrant having area 1.) Give the cdf of V = min{X, Y}. x
10. Use the Laplace transform to solve y" - 3y' +2y f(t), y(0)-0,'(0) 0, where (t)-(0 for 0 st < 4; for t 2 4 No credit will be given for any other method. (10 marks)
solve this Q6: ažu au äx2 + 0. 0 < x <a, 0 < y < b 022 u(0. y) = 1. ut, y) = 1 u(x, 0) = 0, u(x, TT) = |
Let X and Y have join density 6 f(x, y) =-(x + y)2, 0 < x < 1, 0 < y < 1