A Moving to the next question prevents changes to this answer.Question 2Given the system of differential equations-2r2y,+3y,+4e-21then the particular solution of the nonhomogeneous equation is(7) '«y (t)=Ve', where y=(1)OB.y (t)=Ve(7)where y=+21where y=(1)'aPAI=(1) AOD.2.K ay 1= (1)"

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Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Using the method of undetermined coefficients, the general form of the particular solution of the ordinary differential equation y" + 8y' + 16y= (x²+4)e-4x is a. (Ax² + Bx + C)e-4x b. (Ax2 + Bx + C)x²e-4x c. (Ax² + Bx + C)xe-4x d. None of them
We saw that in the nonlinear system of differential equations: the quantity is constant along solution curves. y []-[2²] = X' H (x, y) = -=-=-1² + X 1/1/2x² - 1 ·x³ 3
Solve the system of differential equations. 4 0 x' X 08 x₁ (0) = 2, x₂(0) = 12 x₁ (t) = x₂(t) =
Please solve question number 5 of this image
A system of differential equations has a general solution 3 20t -10t []=[³] Enter an expression in the box below that gives the value of a in the particular solution that satisfies 17 x = and y¹7 when t = 0. = α =
where A system of system of first-order linear differential equations has the form y' = Ay y' = , y = Y1 Y2 , A = a11 a21 This gives us the system B [an an2 ann] Solve the system of linear differential equations by following the steps listed. y₁ = y₁ 432 y₂ = -2y1 + 8y2 a12 022 ain a2n ⠀ (a) We first want to write this as a matrix equation y'= Ay. List out what the matrix A should be in this matrix equation. (b) We would like to have the equations so that y is a function of only y₁ and ₂2 is a function of only y2. To do this, we want to turn A into a diagonal matrix. This can be done by taking the diagonalization of A. Diagonalize the matrix A you created in part a. (c) Now that we have a matrix P such that P-¹AP = D is diagonal, we substitute y' and y to be Pw' = y Pw=y Pw = APw Since P is invertible, we can multiply P-1 to the left on both sides of the equations to get w = P-¹APW = Dw Write out what the system of linear differential equations looks like now. (d) Let k be any scalar.…
Which of the following systems could be used to obtain the solution to the differential equation y" - Sy" + Sy' - 2y = 0? (A) X = }3 (B) { = >2 (C) = y3 (D) = 2 - Sy- Sy2+ 2y3 (G) - y3 *= 1 *- Sy1 + 2y2 - Sys = 2y- Sy2 Sys - Sy - Sy2 + 2y3 y = 2y1 – Sy2 - 8ys (E) = 2 (F) - 3 (H) ý = 32 * = 91 *= 2y1 + 8y2- 5ys *= 2y1 - Sy2 - Sys = Sy1 + 2y2-Sy3
SOLVE STEP BY STEP IN DIGITAL FORMAT 2. The solution of the differential equation 4 0x² a) U(x, y) = sen(x - 2y) b) U (x, y) = 8²U dy² 0 (2x - y²) c) U(x, y) = (x2² - 2y)
(2) Solve the initial value problem = -₁ +42₂. = -411-12; 2₁ (0) = -2, 1₂ (0) = 2 by transforming the system into a single differential equation of second order. I'2
The differential equation +5-24y = 0 has auxiliary equation with roots -8,3 Therefore there are two fundamental solutions Use these to solve the IVP 2 m² +5m-24 = 0 -8x 3x e d²y dx² dy +5- - 24y = 0 dx y(0) = 6 y'(0) = 1 y(x) = 4
The general solution to the differential equation y"+e²x-6)y=0 has the form 2x-6)y=0 y=C₁ Ja (f(x)) + C₂ Ya (f(x)). Find the value of a and the function f(x). and a = f(x) = Hint: Try using a new independent variable z=ex.

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