0.5 -0.5 1A) Using the direction field graph below, find y(2) if y(0) = 0. (Note the vertical and horizontal lines are the y and x axis. Three solution curves are drawn). Answer_ 18) Find y(2) if y(0) =2. Answer G A 1 1 -0.5 0 1 0.5 11 7111 1.5 17 1 1 1 1 1 11 1 2.5 1 1 1 1 1 1 1 1 1 1 t 1 1 1 1 t 1 1 1. 1 1 1 ↑ 1 3.5 1 † ↑ 1 1 f 7 1
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- A mass m moves along the x-axis subject to an attractive force given by 19mx/2 and a retarding force given by , where x is its distance from the origin and is a constant. A driving force given by , where A is a constant, is applied to the particle along the x-axis. Write down the equation of motion. What value of results in steady-state oscillations about the origin with maximum amplitude? What is the maximum amplitude? what is the Q value?Sketch the direction field of the differential equa tion.Then use it to sketch a solution curve that passes through thegiven point. y' = x - xy , (1,0)Find the orthogonal trajectories of the one parameter family of curves ex+e-y=c
- find orthogonal trajectories of the given family of curves // hallar trayectorias ortogonales de la familia de curvas dadas a) x 1/3 + y 1/3 = c b) 2x 2 + y 2 = 4cx Solve Nonhomogeneous Differential Equation by Superposition Method // resolver Ecuacion diferencial no homogenea por metodo de superposición y '' + 25y = 6sen (x)obtain a slope field, and add to it graphs of thesolution curves passing through the given points. y' = 2( y - 4) with (0, 5)Please Please Please do this by hand with a sketch of the graph. I know that 5 and -4 are the critical points, and that 5 is stable and -4 is unstable. I am looking for the justification for that as well as a hand-drawn (neat) sketch of the direction field, as well as the graph of the solution curve through y(0)=3. Thank you for your help
- A spherical dust particle, with a radius a=0.11mm and density of 1030kg/m3, is sedimenting in the quiescent air that has a viscosity of μ=1.81×10−5 kg/m⋅s. The particle experiences the gravitational force, with g=9.81m/s2, as well as a friction force from the viscous air that can be described by F=−6πμaU, where U is the instantaneous velocity of the particle. The motion of the particle is governed by the Newton's second law. At the time t=0, the dust particle has a downward speed of 0.17m/s. Use the Euler's method, and a time step of h=0.1s, calculate: When t=0.1s, the downward speed of the dust particle is m/sFor what values of the constant k does the Second Derivative Test guarantee that ƒ(x, y) = x2 + kxy + y2 will have a saddle point at (0, 0)? A local minimum at (0, 0)? For what values of k is the Sec-ond Derivative Test inconclusive? Give reasons for your answers.Draw the slope fields of dy/dt = -t2y at integer values ( y is greater than or equal to -5 and less than or equal to 5 and x is greater than or equal to -5 and less than or equal to 5). Sketch the solution curves with initial values y(0) = 2 y(0) = -2 y(-4) = 3 y(-4) = -3
- Find the orthogonal trajectories for the family of curves (enter your solution in the form: F(x,y)=c or y=F(x,C) Where C is a needed constantcalculate y(0,1) with the interval Δx = 0.025 using the Euler methodsdetermine the equation of the orthogonal trajectories of the following families curves: The cissoids, y^2=x^3/(a-x)