Explanation Given: The initial-value problem f ' ( x ) = f ( x ) , f ( 0 ) = 3 . Concept Used: Power rule of integration : ∫ x n d x = x n + 1 n + 1 ∫ sin x d x = − cos x Calculation: In order tosolve the given differential equation f ' ( x ) = f ( x ) , observe that the solution will be a function whose derivative is the function itself

5th Edition

ISBN: 9781429241861

Author: Laura Taalman, Peter Kohn

Publisher: W. H. Freeman

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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 differentia…

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Chapter 4.7, Problem 8TF

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The solution of the initial-value problem f'(x)=f(x), f(0)=3

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Chapter 4.7, Problem 7TF

Chapter 4, Problem 1D

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17. Consider a mass-spring system that satisfies 2y′′(t) + by′(t) + 50y(t) = 0.Which of the following is/are true?(i) If b = 0, the motion is critically damped with period π/5 .(ii) If b = 12, the motion is underdamped.(iii) If b = 40, the motion is overdamped.A. (ii) and (iii) only B. (ii) only C. (i) and (ii) only D. (i) and (iii) only E. All

20. Find the general solution to the differential equation y(4) − 8y′′ + 16y = 0A. y = c1e^2x + c2e^−2xB. y = c1xe^2x + c2xe^−2xC. y = c1e^2x + c2e^−2x + c3xe^2x + c4xe^−2xD. y = c1xe^2x + c2xe^−2x + c3x^2e^2x + c4x^2e^−2xE. y = c1 cos 2x + c2 sin 2x + c3x cos 2x + c4x sin 2x

9. A 1 kg mass is attached to a spring with constant 13 N/m. The system is immersed in amedium which offers a damping force numerically equal to 6 times the instantaneous velocity.If x is the displacement of the mass from equilibrium, measured in meters,then x′′ + 6x′ + 13x = 0 . Which of the following statements is true?A. x(t) = c1e^−t + c2e^−5t, and the system is underdamped.B. x(t) = c1e^−t + c2e^−5t, and the system is overdamped.C. x(t) = c1e^−3t cos(2t) + c2e^−3t sin(2t), and the system is underdamped.D. x(t) = c1e^−3t cos(2t) + c2e^−3t sin(2t), and the system is overdamped.

Chapter 4 Solutions

Calculus

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The solution of the initial-value problem f ' ( x ) = f ( x ) , f ( 0 ) = 3

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The solution of the initial-value problem f'(x)=f(x), f(0)=3

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Chapter 4 Solutions