c)QUESTION 3a)Use the method of Laplace transform to solve(2, 0<1/2where y(0)-3,(0) -1.b) Use convolution theorem to find{2+}Use Laplace transform to solve the following system of differentialequationsdz-2y= cos 2t,dtdy+2x-sin 2t,dtgiven that x = 1 and y = 0 when t = 0.

📍 Approach to solving the question: Question 3(a) Using the properties of Laplace transform: L{y′′}…

Answered: c) QUESTION 3 a) Use the method of…

Calculus: Early Transcendentals

8th Edition

ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

Section: Chapter Questions

Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...

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9
Determine the solutions of the following first-order ODEs: Tip:y'=xv'+v y=xv * xv'+v=(4xv-3x)/(2x-xv) >>>> xv'+v=(2v-3)/(1-v)>>>xv'=(2v-3-v+v²)/(1-v) * >>>>>>>>>** ANSWER CORRECT :|y − x| = C|y + x|3 **<<<<<< *****The answer |y − x| = C|y + 3x|5 is considered wrong ( will not be accepted as it will be considered wrong)*****
Question 9 Find the solution of the integro-differential equation using Laplace Transform: y" + 4y' + 3y = 2 e-tdt;y(0) = 0,y'(0) = 0 %3D Oy = (4 – 3e(1+ 2t) – e-3*] Oy = (4+ 3e-(1– 2) – e-3«] Oy = (4+ 3e (1 – 2t) – e*] Oy = }(4 – 3eʻ (1 + 2t) – e*] %3D
Please show all working out on paper and leave some explanations
Los(2a) = 2 cos²a - 1 cos(2a)=1-2 sin² a Ys tk+1=nCkx"-kyk. ding powers of x, the general term sion of (x + y)", written in tan(2α) = 2 tan a 1-tan² a y = a sin[b(x-c)] + d y = a cos[b(x-c)] + d D. x-6 C. x-5 9. For the polynomial function f(x)=x³ - bx² + cx-24 where b,cel, all of the following are B. X-4 potential factors except: A. x-3 f(x) is shown where a 0 and c> 0, then a potential equation might be: Vos²a - sin² a
The characteristic equation of the ODE y(3) -2y'+y?=0 is defined by p3 – 2 =0 p – 2r+1=0 r³-2r=0 3-2r²+r=0
Consider the partial differential equation D( a²C _10C 1 ƏC + V Or? r ôr C'= C,x= 0 0,r = 0 - D Or KC,r =1 Apply the Laplace transformation and write the general form of the solution in the Laplace domain (do not try to invert).
2c
part 2) a) Solve y" -6y' +9y=0. b) Find the particular solution of y"-6y' +9y=3-t c) Use the Laplace transform to solve the given initial value problem y"-6y' +9y=3-t, y(0)=0, y' (0) = 2

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c) QUESTION 3 a) Use the method of Laplace transform to solve (2, 0<1/2 where y(0)-3,(0) -1. b) Use convolution theorem to find {2+} Use Laplace transform to solve the following system of differential equations dz -2y= cos 2t, dt dy +2x-sin 2t, dt given that x = 1 and y = 0 when t = 0.