(a) Find the general solution of the motion of a mass attached to the ceiling by aspring in presence of friction, i.e. solve the ODEmi = mg -k(y-l) — yy.with m = 1, k = 3, y = 2, g = 10, 1 = 5, where y indicates the distance of the massfrom the ceiling.(b) What is the limit lim y(t) for the motion of the mass described in (a)?Describe in words the asymptotic dynamical behaviour of the mass for t→∞.(c) Determine whether the differential equation8x12 y ² + y cos(x) + (yx + sin(x) — e³) y' = 0-is exact. If it is exact, find its general solution in explicit form.[1

Answered: Image /qna-images/answer/c29f7cfc-caf3-4fcf-a64d-13e64dad6a02.jpg

Answered: (a) Find the general solution of the…

Trigonometry (MindTap Course List)

10th Edition

ISBN:9781337278461

Author:Ron Larson

Publisher:Ron Larson

Chapter6: Topics In Analytic Geometry

Section6.2: Introduction To Conics: parabolas

Problem 4ECP: Find an equation of the tangent line to the parabola y=3x2 at the point 1,3.

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Suppose the solid W in the figure is the spherical half-shell consisting of the points above the xy-plane that are between concentric spheres centered at the origin of radii 4 cm and 10 cm. Suppose the density 8 of the material increases linearly with the distance from the origin, and that at the inner surface the density is 8 g/cm³ while at the outer surface it is 10 g/cm. (a) Using spherical coordinates, write d as a function of p. Enter p as rho. 8(e) = 25/9(rho-4) (5.0 (b) Set up the integral to calculate the mass of the shell in the form below. If necessary, enter o as phi, and 0 as theta. B D CLI 25/9(rho-4)rho^2sinphi "OP Ópdp A = 0 B = 2pi C = 0 D= pi/2 (Drag to rotate) E- 4 F= 10 (c) Find the mass of the shell. 4536pi
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