(1 point) Consider the IVP У + 3ty — бу %3D 3, у(0) — 0, У (0) — 0 (a) What is the Laplace transform of the differential equation, after being put into standard form? Y'(s) ) Y(s) = |(b) What is the solution to the differential equation? y(t)
Find the solution of the initial value problem [y(0)=-1, у"(0)=-3, у "(0)=0, у"(0)-0] a) y--3-х -2x-2x f None of the above.
Consider the following initial value problem у(0) — 0. у%3D х+ у, (i) Solve the differential equation above in tabular form with h= 0.2 to approximate the solution at x=1 by using Euler's method. Give your answer accurate to 4 decimal places. Given the exact solution of the differential equation above is y= e-x-1. Calculate (ii) all the error and percentage of relative error between the exact and the approximate y values for each of values in (i) 0.2 0.4...
3. y" - бу' +9у 3 te3t У(0)%31,у (0)-4
Given a second order linear homogeneous differential equation а2(х)у" + а (х)У + аo(х)у — 0 we know that a fundamental set for this ODE consists of a pair linearly independent solutions yı, V2. But there are times when only one function, call it y, is available and we would like to find a second linearly independent solution. We can find y2 using the method of reduction of order. First, under the necessary assumption the a2(x) F 0 we rewrite...
3. Specify the classes (communication, transient and recurrent) of the following Markov chains, and determine whether they are transient or recurrent: o i o12 o0 0 1 21 0 0 0 11, 310 0 20 1 0 0 00호 310 1 1 2 2/ 3. Specify the classes (communication, transient and recurrent) of the following Markov chains, and determine whether they are transient or recurrent: o i o12 o0 0 1 21 0 0 0 11, 310 0 20 1...
QUESTION 11 +3x Solve the first-order differential equation dy e2y2 = dx у
У"-у,_6y 8. y'(0)-0 -cost y(0)-0 9. y"-y,-6y-3 sin2t y'(0) y(0)-1 0
2. Given two initial value problems, у" — р(г)у +q()у +r(x) with a <I<b,y(a) — с,1 (а) —0 (1) and у" — р(г)у + g(х)у with a < r <ь,y(a) — 0, and / (а) — 1 (2) [a, b) where p(x), q(z) and r(x) Show that given two solutions yı(x), y2(x) to the linear value problems above, (1) and (2), respectively, then there exists a solution y(x) to a linear boundary value problem above where y(a) %3D 0, у...
We will rank the y-values of the following data set: 0 у 10.5 - 11.8 IN -13.9 4 5.9 7 7.6 9.1 11 12.7 -19.8 -24,7 -18.3 -23.6 -27.1 The scatterplot of the data looks like this: MI Problem Set . . . . Fill in the following table: X-rank yrank x 0 y 10.5 1 MI/ Problem Set . . . Fill in the following table: x-rank yrank y 10.5 0 1 ... essments Fill in the following table:...