Assume that Y = e-5+2i)t4iis a solution to the systemdtWhich of the following is a result of applying Euler's formula?= AY%3DY = e 5t-4 sin(2t)2 cos(2t)+i.e-5t 2 sin(2t)4 cos(2t)+i.e-5t 2 sin(2t)4 cos(2t)2 cos(2t)! sin(2t) +i.2 cos(2t)4 sin(2t)2 sin (2t)-4 cos (2t)Y = e-5t-Y = e-5t2 sin(2t)4 cos(2t)+i.e+i.e 5t 2 cos(2t)4 sin(2t)Y =e-5tY =e 5t 2 cos(2t)-4 sin(2t)4 cos(2t)2 sin(2t)+i.e

Euler's formula: Euler's formula states that for every real number x, eix=cosx +isinx Given:…

Assume that Y = e(-5+2i)t 2 4i is a solution to the system dt = AY. %3D %3D Which of the following is a result of applying Euler's formula? TOY=e-5t-4 sin(2t) 2 cos(2t) 2 sin(2t) 4 cos(2t) Ý = e-5t +i.e-5t Ỹ = e-5t 2 cos(2t) -4 sin(2t) 2 sin(2t) 4 cos(2t) +i.e-5t Ý = e-5t 2 cos(2t) 4 sin(2t) 2 sin(2t) 4 cos(2t) +i.e-5t Y = e-5t 2 sin(2t) -4 cos (2t) +i.e-st 2 cos(2t) 4 sin(2t) 2 cos(2t) -4 sin(2t) 4 cos(2t) 2 sin(2t) Y = e-5t +i.e-st

Assume that Y = e(-5+2i)t 2 4i is a solution to the system dt = AY. %3D %3D Which of the following is a result of applying Euler's formula? TOY=e-5t-4 sin(2t) 2 cos(2t) 2 sin(2t) 4 cos(2t) Ý = e-5t +i.e-5t Ỹ = e-5t 2 cos(2t) -4 sin(2t) 2 sin(2t) 4 cos(2t) +i.e-5t Ý = e-5t 2 cos(2t) 4 sin(2t) 2 sin(2t) 4 cos(2t) +i.e-5t Y = e-5t 2 sin(2t) -4 cos (2t) +i.e-st 2 cos(2t) 4 sin(2t) 2 cos(2t) -4 sin(2t) 4 cos(2t) 2 sin(2t) Y = e-5t +i.e-st

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

See similar textbooks

Related questions

Q: 3. Given the matrices 1 - 2 --8-0 1 1 1 X = V and c = 0 1 2 1 1 2 2 A = 0 1 1 B 1 0 1 premultiply…

Q: 1. The following system has one root in the first quadrant. Perform one iteration to calculate the…

A: The Multivariate Newton Raphson method uses the formula: xn+1yn+1=xnyn-∂f1∂x∂f1∂y∂f2∂x∂f2∂y-1×fxnyn…

Q: dz (a) Find of the following functions: dx 2 zxa+!cos y? = sin(yº + 22z) where a - The first digit…

Q: y': 2хy y' = y2 –x²

Q: and cos(3 α₁) + cos(3 a ₂) = 0 cos(a₁) + cos(a ₂) = 2M₁ = 1.6 7.6° and a₂ 52.4°. Using an iterative…

A: We have to find out the value of α₁ and α₂

Q: Quesition 1 is applied to an LTI system with impulse re u(t). Give the output of the system. -2 x(t)…

Q: Which of the following functions are solutions to the 1-D heat equation? Ut = guxx Ou= 2-36t cos(3x)…

A: Given: We will be checking the answers one by one. For : Here, ut=∂ ∂…

Q: 2y +y= 1- CoSx Select one: a. A+B cosx O b. A + B x² + C cosx + D sinx C. A+Bx cosx + Cx sinx d. A+B…

Q: in Figure Q.1 is given by di L=+Ri+-= dt (i) Viti Ri+ = √ [idt = v(t) R i(t) voltage source…

A: Integration is used

Q: 2. Show that for any x, the matrix A = A² = I. 3. Given the matrices A = 1 22 1 2 ---0--0 1 1 B = 1…

A: What is Matrix: a collection of numbers lined up in rows and columns to form a rectangular array is…

Q: dX Find for the given matrix function. dt dX dt sin 5t cos 5t cos 5t e-5t X(t) = sin 5t 8 cos 5t…

Q: . (D³ + 4D) y = 5e +3 cos 2x using MUC ; X

A: As per our guideline, we are supposed to solve only first question. Kindly repost other question as…

Q: The roots of a d.e are -1, 2tV3i What is the solution? O a. y = e*(c, cos 3x + c2 sin 3x) + c3 cos x…

Q: Using complexification, find the general solution of d²y dt2 dy +2- + 5y = 34 cos 2t. dt

Q: 1 ezt dz 2ni Izl=2 z2+1 cos (t) o tan (t) o sec (t) o sin(t) o

A: See the attachment

Q: Which of the following is the correct form of the solution to the non- dy homogeneous equation for…

A: Explanation of the solution is given below...

Q: The function=e is a solution of which of the following system? (C,cos 21+ C sin 2r) Spring mass…

A: Function :

Q: A second order ODE has the following solution y(x) = e* (C, cos (3x) + C2 sin (3x) ) What's the ODE…

A: The given question is related to ordinary differential equations. The solution is explained below.

Q: Assume y=ex cos(3x) is one of the solutions of DE (3)-3y" + 7y-5y=0.Then a + B is:

Q: B. Non- homogeneous Higher Ordered LDE 2. (D°+ 180 - 34 y = 25 x2 + 10 e* cos 4 x %3D

Q: By using the unlimited coefficients method, choose the correct answer for this equation y"-y'-2y=0…

Q: If find az/au and az/av. дz/?u Əz/dv= z = sin(x² + y²), x = u cos(v), y = usin(v), REMARK. This…

Q: Consider the IVP y"(t) − 2y'(t) + 5y(t) = 0, y(0)=-1, y'(0)=3 (a) The characteristic equation of the…

Q: Which of the following equations can be rearranged into separable equations? O y – y? = t - O y +…

A: y' + yt² = t² can be written as separable equation as : y' = t² - yt² So, y' = t²(1-y) So, dy/(1-y)…

Q: 2. Show that for any x, the matrix A = A² = I. [cos(2x) sin(2x) [sin(2x) - cos(2x)] satisfies the…

A: Here we have to show that for any x the matrix A=cos(2x)sin(2x)sin(2x)-cos(2x) satisfies the…

Q: ()- 42 X; X(0)= -30 is The solution of the system X': %3D

Concept explainers

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.

Question

Assume that Y = e-5+2i)t
4i
is a solution to the system
dt
Which of the following is a result of applying Euler's formula?
= AY
%3D
Y = e 5t-4 sin(2t)
2 cos(2t)
+i.e-5t 2 sin(2t)
4 cos(2t)
+i.e-5t 2 sin(2t)
4 cos(2t)
2 cos(2t)
! sin(2t) +i.
2 cos(2t)
4 sin(2t)
2 sin (2t)
-4 cos (2t)
Y = e-5t
-
Y = e-5t
2 sin(2t)
4 cos(2t)
+i.e
+i.e 5t 2 cos(2t)
4 sin(2t)
Y =e-5t
Y =e 5t 2 cos(2t)
-4 sin(2t)
4 cos(2t)
2 sin(2t)
+i.e

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

SEE SOLUTION Check out a sample Q&A here

Step 1: Given.

VIEW

Step 2: Express the solution using Euler's formula.

VIEW

Step by step

Solved in 2 steps

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

$Differential Equation$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, advanced-math and related others by exploring similar questions and additional content below.

Similar questions

A linear, time-varying mathematical model is A. 4 (1– sin 2t) + 2x² = 0 B. 4 + 2x? = sin 2t dx C. 4 + (1 – sin 2t) 2x² = 0 dt dx D. 4 + 2(1 – sin 2t) x = sin 2t
- 2t A particular solution of the equation y" + y − 2y = 3te¯ + cos(2t) has the form -2t (At+B) + Ct cos(2t) + Dt sin(2t) e-2t (At² + Bt) + Ct cos(2t) + Dt sin(2t) e−²t (At² + Bt) + C cos(2t) + D sin(2t) O e 2t (At+B) + C cos(2t) + D sin(2t)
The general solution of y +5Y3D3 is: Select one: a. y= C cos 3t Ob. eSt +e 5t O C. y=3+ Csin 5t d. 13. +Ce-5t Exam
Which of the following is a possible solution of y- 4y = 0 O y = -2 cos(x) Oy=-e2 O y= e O y = -2 sin(z)
the the solution of a 2nd order linear ODE with constant coefficients (see picture for rest of question)
3X y+5y+y -2X =3e + e এ) -29 +9 =X -C %3D %3D (10 +2y+4y= 10 Sin3X %3D (2) +4y = gSia 2x
#2
The solution of the equation In(3z – i) = −3+2i is - ○ a. ¹³e¯³ cos2+i+i½³e¯³sin2 O b. e³ cos2+i+ie³ sin Oce³cos2-1+ ie³ sin2 -3 O d. e³ cos2+ i(e¯³ sin2+1)