Question 6: Score 0/1 Use the transformation U = y(x) - 2+4 to find the solution to the initial value problem (a) - 92)-+10 9(a)-071 y(4) = 4 (I) = Your response No answer Correct response x+2"(3 x-8)(1/2)-4 Grade: 0/1.0 Only enter precise Maple syntax as explained in the Guide to Online Maple TA Tests. In particular, remember that the basic arithmetic operations are +,- /and. Please note that you CANNOT omit 3x is not correct, 3x is. Total grade:...
Solve the following initial value problem 1 2 3 4 01 63 0 012 x +e' 0001 o x(0)0 Solve the following initial value problem 1 2 3 4 01 63 0 012 x +e' 0001 o x(0)0
1. (25%) Solve the initial-value problem. zdy + 10y = 5; y(0) = 0 4 dt
Solve each initial value problem 4 (c) y" - 2y' y te4, y(01, y'(0)1
9. [20 pts.] Recall that 1 +tAk.. 1 etA I+tA+tA2 2! k! (a) Compute e4 explicitly if -G:) A= 1 0 HINT. Recall the expansions: e = 1 + t + +3+ et = 1 -t+ 3++ tk (b) Use your result from (a) to write out the solution (t)=(x1(t), x2(t)) of the initial value problem: k! () T(O) 1 0 C2 For what initial values (C1, C2)" is it true that (t) 0 as t oo? - 9. [20...
Let y,p ~iid Exp (0), for i = 1, . . . , n. (p(y|0) for 6 to be Gamma(a, b), tha distribution of θ BeAy). Assume the prior distribution Find the posterior 2. t is, p(0) -ba/ra)ge-i exp{-be. 3. Find the posterior predictive distribution of a future observation in problem 2
Let Lyl = y + 2y + y (a) Solve the initial value problem L[y]=0 y(0)=1 (y'0)=1 (b) Use the method of undetermined coefficients to find a particular solution to the equation L[y] =2e-4
Suppose X1, X2, Xz~exp(1) and they are independent. (a) Compute the cdf of X1 (b) Let Y- max(Xi, X2, X3). Find the cdf of Y (c) Derive the pdf of Y
5.Solve the initial value problem y" +5y' +6y-g(t), y(0) 0,(0) 2, where (t)-t 1<t<5,. 1, 5 < t. Then sketch the graph of the solution. (Use technologies. Be sure the graph is neat.) Sec. 7.6.39]
5. Random variables X U[0, 1 and Y ~Exp(1) are independent (a) Compute P(X Y > z) for the case 0 S1 and the case z >1. b) Compute and plot the pdf of XY. (c) Give the MGF of X Y. 5. Random variables X U[0, 1 and Y ~Exp(1) are independent (a) Compute P(X Y > z) for the case 0 S1 and the case z >1. b) Compute and plot the pdf of XY. (c) Give the...