Exercises 17.1.1. Which of the following equations are separable?a. ý = sin(ty)b. y = e¹eªc. yy=td. y = (t _ t) arcsin(y)e. j= t’ lny+43 Iny2. Solve j = 1/(1+t). =3. Solve the initial value problem y = t" with y(0) = 1 and n ≥ 0. ⇒4. Solve y = ln t. ⇒

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Answered: Exercises 17.1. 1. Which of the…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

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3.) Imagine a string that is fixed at both ends (for example, a guitar string). When plucked, the string forms a standing wave. The displacement, u(x, t), of the string varies with position x and time t. Suppose a,t) = 2sin(xx)sin() for 0 0. At a fixed point in time, the string forms a wave on 10, 11. Alternatively, if you focus on a point on the string (fix a value of r), that point oscillates up and down in time. a.) What is the period of the motion in time? За.) du 3b.) dt b.) Find the rate of change of the displacement with respect to time at a constant position (which is the vertical velocity of a point on the string.) 3c.) x = c.) At a fixed time, what point on the string is moving fastest? 3d.) t = d.) At a fixed position on the string, when is the string moving fastest? du 3e.) e.) Find the rate of change of displacement with respect to position at a constant time (which is the slope of the string.) 3f.) r =, f.) At a fixed time, where is the slope of the string the greatest?
8. Theorem h° = i° = j° = 30
nJI = (3x + 2), mHLK = (15x- 36)', and mZHMK = (8x – 1)', find mh %3D %3D %3D M K I 138 O 140 O 204° O 151 1 2 3 4 5 6 7 8 9
A wheel is rotating at a rate of 40 revolutions per minute. Find the angular speed of the wheel in radians per minute. Round your answer to two decimal places. i) 125.66 ii) 251.33 iii) 14400 iv) not listed O i i O iv
b. A particle moves in simple harmonic motion according to the equation, S = 09A cos(wt) + 09B cos(wt). Where s is the displacement, w is the angular d2 +ws=0. 'dt2 frequency and A, B are constant. Show that,

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Exercises 17.1. 1. Which of the following equations are separable? a. y = sin(ty) b. y = e¹ey c. yy=t d. j= (t* _ t) arcsin(y) - · e. i t²lny +4t3³ In y =