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- Write down two linearly independent solutions of the Bessel equation 16x?y" + 16ry + (162 – 9) y = 0.The position vector of a moving particle, at time t is given by 7 - 2 27- 10 t+4 (2 +2t) k (Answers must all be given in exact form.) (a) At what time does the particle pass through the point (8, –20, 32)? (b) Find the velocity vector of the particle at this point. Give your answer in the form: ai + b*j + c*k (c) What speed does the particle have when it passes through this point? 固助Solve y" - 5y' + 6, using characteristic equation.
- Use Newton's method with the starting point (1,2)T to find a solution of the system +y 0 2+y = 1. The first iteration produces the vector (A) (2,2)T (B) (2,1) (C) (1,1)" (D) (1,2)" (E) none of the above O (A) O (B) O (C) O (D) O (E)Find the parametric equation of the line through a parallel to b, using t as the parameter. -2 - 6 THU b= a = 2 X= + (Type an integer or a simplified fraction for each matrix element.)Re(z²) = 1
- #7Consider the initial value problem: 3t æ+g(t), æ(1) = (). (-3 4t2 -3 -2t + a Suppose we know that æ(t) -3t + B) is the unique solution to this initial value problem. Find the constants a and B and the vector function g(t). α ) g(t)Solve the particular solution (D2 + 3D + 5)y = 5e-x sin (2x) using D - operator method.