5. The solution to the system X-Ax can be written as etAX(O), where the matrix function etA İS defined by the series etAA)tA) Given the matrix tA- etA (part of Lebl 3.8.2)? 3t t t 3t , what is 3! 2! 5. The solution to the system X-Ax can be written as etAX(O), where the matrix function etA İS defined by the series etAA)tA) Given the matrix tA- etA (part of Lebl 3.8.2)? 3t t t 3t , what is...
Find a fundamental matrix for the system x'(t) = Ax(t) for the given matrix A. A 01 0 0 10 0 0 0 0 0 1 00 - 29 10 et 0 0 el 0 -t 0 et 0 0 et O A. X(t) = 1 0 OB. X(t) = 0 51(5 cos 2t - 2 sin 2t) e5t (5 sin 2t+2 cos 2t) 0 0 2t2 cos 5t - 5 sin 5t) 2 (2 sin 5t + 5 cos...
Please help me solve this, thanks! Find the general solution to the system x' = Ax where A is the given matrix. | -2 -2 -6 A= 0 0 6 | 0 -2 -8 b) X(t)=( X(t)= Ce 0 e) X(t)= C, e 20 +46?' -6 +2° -1 | 2 f) None of the above. Find the general solution to the system x'= Ax where A is the given matrix. 0 1 0 A= 0 0 1 | -20 16...
(17 points) Match the third order linear equations with their fundamental solution sets. 1. y" - Y" - ' +y=0 2. y'" - 5y" + 6y' = 0 3. ty" - y" = 0 4. Y" + y 0 5.Y" - 6y" + y - by = 0 6. Y" + 3y" + 3y + y=0 A. e , te, tet B. e, cos(t), sin(t) C. 1, cos(t), sin(t) D. 1, t, 13 E. et, tet, et F. 1, 2,...
QUESTION 4 One solution of x' = The general solution is 1 2 e3t ОА. + C3 e3t Int x+b(e) is x(e) = [7] 0 [8]+ole [l] to (o) ( OB + Ci Int] et + e3t OD ci Int OC e3t Ci + C2 + C3 Int
QUESTION 4 One solution of x' = The general solution is 1 2 e3t ОА. + C3 e3t Int x+b(e) is x(e) = [7] 0 [8]+ole [l] to (o) ( OB + Ci Int] et + e3t OD ci Int OC e3t Ci + C2 + C3 Int
Match the third order linear equations with their fundamental solution sets. 1. y????y???y?+y=0 2. y????5y??+6y?=0 3. y???+3y??+3y?+y=0 4. ty????y??=0 5. y???+y?=0 6.y????2y??+y??2y=0 A. 1, cos(t), sin(t) B. e?t, te?t, t2e?t C. 1, e3t, e2t D. e2t, cos(t), sin(t) E. et, tet, e?t F. 1, t, t3
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...
(1 point) Match the functions with the parametric curves labeled A†H. You may want to click on the thumbnail image to produce a larger--and correctly scaled--image in a new window. [ 2 + ] ! !! 1. f(t) = [ 43+1] 2. f(t) = 2 cos(t) | 3 sin(t) ] cos' (t) ] 3. f(t) = sin (1) 4. f(t) = et cos(t)] Le-sin(t) ] 5. f(t) = 3t – sin(t) ] 3 – cos(t)] te- 6. f(t) =...
Determine the form of a particular solution of the equation. 4, NA+B+ Ct+D)+l u-AB2+C+D+ Ee13 up-A+ B+Ee13) Find the general solution of y" 14y' +58y 0. y- ce cos(31) +ce sin(3) y-ce cos(3t) + eze 'sin(31) y ce cos(3t) + ce"sin(3t) y-cje"cos(3t) + czesin(3t) -7t 7t Find the general solution ofy"-3'-28y-0. y(t) = cer + cze-41 Find the general solution ofy"- 130y 0. JC1 + c2e130r ycie +te130r Find the general solution of y"-30y' 225y 0. cote 15t 15t 15t...