Problem 7.4. Solve the following IVP's. 2t 10 e 8.e a) 7.y10e Yo = 4 b)...
(3) Determine by substitution which of the functions ya(t) = A e(-2+6j)t, yo(t) = B e(2+63)t, yo(t) =C e(-2-63)t satisfy the DE y" +4y'+40 y = 0, where A, B, C are nonzero constants. (4) Let y(t) = 0 + A e(-2-63)t + Be(-2+63)t, and use Euler's identity to show that y(t) = 0) + C e 2t sin (6t) + De-2t cos (6 t), where C =j(B-A) and D equals something similar. Then find constants C, D such that...
Solve the given initial-value problem. dax + 4x = -7 sin(2t) + 6 cos(2t), x(0) = -1, x'(0) = 1 xce) = -cos(2+) – sin(2t) + {cos(21) + (sin(21) Need Help? Read It Watch It Talk to a Tutor
need help all those questions. 10. Solve the following systems of linear differential equations: 11. Determine the Laplace transform of each of the following functions: (a) fe)-2t+1, 0StcI , 21 (b) f(t) te (c) f(t) = cos t cos 2t (Hint: Examine cos(a ± b).) Determine the inverse Laplace transform of each function: 12. (a) F(s) = 52 +9 is Demin 13. Determine L{kt cos kt + sin kt). 0, t< a 14. Determine L(cos 2t)U(t-r), where U(t-a)={ 15. Use...
please complete all parts Problem F.7: These are independent problems (a) (5 points) Solve the following integral. (Hint: Think Fourier series.) (cos(nt) - 2sin(5rt)e-Jr dt XCj) (b) (5 points) Find the Fourier transform io of the following signal: 2(t) = sin(4t)sin(30) (c) (5 points) Solve the integral: sin(2t) 4t dt (d) (5 points) Use Parseval's theorem and your Fourier transform table to compute this integral: Problem F.7: These are independent problems (a) (5 points) Solve the following integral. (Hint: Think...
use the Laplace transform to solve the given initial value problem: Only problem 4,8 and 12 please 4. y" – 4y' + 4y = 0; y(0) = 1, y'(0) = 1 5. y" – 2y' + 4y = 0; y(0) = 2, y'(0) = 0 Σ Answer Solution = e 6. y" + 4y' + 297 - 2t sin 5t; y(0) = 5, 7. y" +12y = cos 2t, 22 # 4; y(0) = 1, : > Answer > Solution...
The following IVP will be used for Question 1 and Question 2 on this quiz. Solve the initial value problem using the method of Laplace Transforms. y' - y' = 6x y(0) = 2,y'(0) = -1 The solution will be accomplished through answering the two questions below. In using the Laplace Transform to solve the above IVP, solving for Y(s) gives Y(8) = Y(s) = + 8+3 $-2 s-2 Y(s) – + 5 $+2 8-3 3 5 Y(s) = +...
10 sin 2t if 0 <t< 4. (a) Let r(t) if t > T Show that the Laplace transform of r(t) is L(r) 20(1 - e - e-78) 32 + 4 (b) Find the inverse Laplace transform of each of the following functions: s – 3 S2 + 2s + 2 20 ii. (52 + 4)(52 + 25 + 2) 20e-S ini. (s2 + 4)(52 + 25 + 2) (c) Solve the following initial value problem for a damped mass-spring...
This is question #4 for the key reference, Please help me understand this problem? 8. Find the solution of the initial value problem y" + y + y = 0, y(0) = 3, y'(0) = 1. A. y(t) = 3eź cost – jeź sint B. y(t) = 3et cos – 4e sin C. y(t) = 3e + cos į +8e-t sinį D. y(t) = 3e-t cos į + e-t sin E. y(t) = 3e-ź cost + e-ź sint ANS KEY...
Please solve the problem 8 only by using matrices a,b,c&d in problem 7. 7. Use elimination by pivoting to find the inverse of the following mati ces. T 2 3 2 (b) 2 24 -154 -2 ?24-27 (c)2 3 (d)1 24 5 4 6 L-213 1 1 47 (f) 3 5 2 (e) 2 1 3 5 2 5 8. For each matrix A in Exercise 7, solve Ax b, where b - [10, 10, 10].
QUESTION 3 After use Laplace Transform to transform the following initial value problem X" +x=e-t, x(0) = 1,x'(0) = 1, S-2 you should get X(s)= (write fraction as (S-2)/(5-4)(8+6) for -). Then, find (s-4)(8+6) x(t)= L-?{X(s)}= (write 5/6 by 5 -30 6' e^{-3t} by e and sin(2t) or cos(3t) by sin(2t) or cos(3t)).