Answered: X= [+] -3 1 X × ² = [ 2² -4 ] X…

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X= [+] -3 1 X × ² = [ 2² -4 ] X X2-26-561 est

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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Question

The two given vectors satisfy the given system of linear differential equations. But do they form a fundamental solution set to the system? Please use the Wronskian to calculate

x₁ = Le
x'= [²2²
Do X₁ and X₂ Form
-2t
e-2x
-4
X.
]X
-st
-2e
-5€
Just
the dis
of the
a fundamental Solution Set?

With integration, one of the major concepts of calculus. Differentiation is the derivative or rate of change of a function with respect to the independent variable.

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I asked ChatGPT to solve the second order linear non-homogeneous equation y"+2y+y= = 2x Is the solution that ChatGPT offers correct, or is there one or more mistakes in the work? If the work is correct, verify the solution. If it is incorrect, identify the exact place(s) where the mistake(s) occur. Explain your answer clearly! Below is the response from ChatGPT: Yes, I can solve the equation y"+2y+y = 2x. One way to solve it is to use the characteristic equation method. To find the characteristic equation, we set the left side of the equation to zero and solve for the roots of the characteristic equation, which is given by: r² + 2r + 1 = 0 Solving for the roots, we get: r₁=1+√-1-4--1+√-5 and r₂ =-1-√√-1-4 =-1-√√-5 So the roots are complex conjugates, which means the general solution of the homogeneous equation will be of the form: Yn(x) = e¯² (c₁ cos ( √5x) + ₂ sin (√5. x)) Where c₁ and c₂ are arbitrary constants. To find a particular solution, we can use the method of undetermined…
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