By using the Laplace transform to solve the system (x' 3x-3y+ 2 x(0) = 1 ly' = -6x-t y(0) = -1 We obtain: O x(t)=1/36-1/6 t+133/108 e^t-7/27 e^(-t) and y(t)=3/4-1/6 t-133/108 et-14/27 e^(-3t) x(t)=1/36-1/6 t+133/108 e^6t-7/27 e^(-3t) and y(t)-3/4-1/6 t-133/108 e^6t-14/27 e^(-3t) O None of them x(t)-1/6-1/6 t+133/108 e^7t-7/27 e^(-3t) and y(t)=3/4-1/6 t-133/108 e 6t-14/27 e^(-t)

Q: Given a second order ODE equation of a beam. d²y dx² 7200y (30,000000)(120) = (5400)x(75-x)…

A:

Q: y''+y'=0 where y(0)=0, y'(0)=1 laplace transform of derivatives

A: Given that:-  y" + y' = 0 and y(0)= 0, y'(0) =1 We find laplace transform of this differential…

Q: dz (b) Determine the by using the Chain rule with the following information: ds z = cos (rªy^) – sin…

A:

Q: D) Factor f (x) = x³ + 2x2 + 4x +8 into complex linear factors. %3D

A:

Q: f (x) = 2x+7 if -5=Xcl 8 If X = 1 14X=3 if 11x-2 31 If x > 3 IS this continuous at X=1 ? formula…

A: Any function f(x) is continuous at x=a if  lim x -> a f(x) = f(a) i.e. Functional value at that…

Q: FIND M'(3) = Page 2 of 4 -1 6 2 g(x) • F(x) LET M (x) = F (g(x)) AND V(x) = 9 (f(x)) 6 FIND V'(3) =

A: Step 1: Step 2: Step 3: Step 4:

Q: (b) (2, -5π/6) (r, 0) = (r, 8) = y -1 -2 -3 -5 -1.5 (r> 0) ] ) (r< 0) 1 -1.0 2 3 -0.5 4 y -0.2 -0.4…

A:

Q: 30. E=2*10^5 I=30000 L=600 W=25 y = dy dx = W 120EIL 3 (-x ² + 21³x² - (^x) W 120EIL (-5X² +…

A:

Q: The characteristic equation of the ODE y (3) -2y'+y?=0 is defined by

A: Giveny(3)-2y'+y2=0

Q: a) If L-{F(s)} = f(t) and L-1{G(s)} = g(t), and if a and B are constants, then L-1{aF(s) + BG(s)} =…

A: If L[f(t)]=F(s), then f(t) is called the inverse Laplace transform of F(s). That is; f(t)=L-1[F(s)]

Q: Chapter 4] If f(x) = dt, where g(x) = 1," (÷) V1+t3 [1 + sin(t²)] dt, find f'

A:

Q: Find Solution of Homogeneous linear ODE s (D°, 60 +131 Jy

A:

Q: (4xy+5y)dx+(4x² +15xy-12y)dy=0. Use two methods.

A: Note: according to our guidelines we can answer only first question because there are multiple…

Q: Performing iterations on (25) respectively, leads to the following: n-1 X2km+j v; II n-1 Y2km+j…

A: Given: 2km+j=2km+j2+rj To find: Corresponding equation

Q: x(t) = Find real-valued closed formulas for the trajectory x(t + 1) = Ax(t), where -4 ^-[33] -4…

A: This is an homogeneous linear differential system. We will solve by this using eigenvalues and…

Q: By using the Laplace transform to solve the system x' = 3x - 3y + 2 We obtain: * None of them…

A:

Q: E=2*10^5 I=30000 L=600 W=25 y = dy dx W 120EIL = 120 FIL (-5X² + 6(³X²-1²) ū assume as р 38, P = =…

A:

Q: Assume that  dx1/dt= x1(10-2x1-x2) dx2/dt= x2(10-x1-2x2) a) Graph the zero isoclines. b) Show…

A: Given- Assume that  dx1dt = x110 - 2x1 - x2dx2dt = x210 - x1 - 2x2 To find-  Graph the zero…

Q: f'(x) = = Lº 1 + sec(7t) dr f(x) = sec (2) + 6 X Vì Hint: +== f*√²- 1 + sec (7t) dt = - √1+ sec(71)…

A:

Q: Michelle draws a restangle with a length of 6 cm. She draws a second rectangle with a length of 11…

A: Michelle draw 1st rectangle of length =6 cm 2nd rectangle=6+5=11cm And so on, she keep drawing more…

Q: (4x² + y²) dx + x(x-2) dy =6 Verify that M(x,y) = 4x² + y² and N(x, y) x (x-2) are homogenous 1-

A:

Q: Exercise 1. A student is asked to prove If m is even and n is odd, then m² + n² is odd. 2 The…

A: Let us answer above questions