Find a solution 2. yy' = x(y2 + 4).
Problem 1. (5 marks; 3, 2) Assut Y Y2, YY are a random sample of normally distributed random variables with mean 0, and variance σ2. The following are two estimators of the population variance, σ2 に! b) Derive the mean square error of both Si and S2
Chapter 5, Section 5.2, Question 2 In the Problem: • a. Seek power series solutions of the given differential equation about the given point xo; find the recurrence relation that the coefficients must satisfy. . b. Find the first four nonzero terms in each of two solutions yn and y2 (unless the series terminates sooner). • c. By evaluating the Wronskian W[y1, y2](xo), show that y, and y2 form a fundamental set of solutions. • d. If possible, find the...
2: (a) Find all solutions (x, y) = Z2 to Pell's Equation x2 – 29 y2 = 1. (b) Find all solutions (x, y) € Z to the Pell-like equation x2 - 21 y2 = 4.
Problem 15. Find the general solutions of the following linear ODES. (1) g" +3y + 2y = cos 7. (2) y" - y = sin r.
Vector field F = î 3y + ŷ (5 – 2x) + î (22 – 2) is given. Find: (e) The surface integral of the normal component of the curl of F over the open hemisphere x + y2 + z = 4 above the x-y plane.
1. (10 points) Consider the autonomous equation dy = y2 + 3y + 2 dc (a) (6 points) Determine the equilibrium solutions of the equation, and classify each as asymptotically stable or unstable. (b) (4 points) Sketch at least three solutions to the equation, choosing initial points not corresponding to the equilibrium solutions. Include the equilibrium solutions in your sketch.
Find general solutions of the differential equations to x. 14. xy ry-уз 15. y +3y 3xe3 16. y 2-2xy y2 18. 2x2y-rly,-: уз 20. xy' +3y 3x-3/2 11. x2ys xy + 3y2 25. 2y + (x +1)y'-3x +3
1. Find the volume of the solid bounded by the paraboloids 2 = r2 + 3y² + 1 and 2 = 5 – 3.r2 - y2.
5. (2 Points) Let -2 -y F (x2+y2+z2)2/3' (2+y2)2/3' (r2+y2+22)2/3 Find the work done by this force field on an F(t) = (1+3t, 1 + 4t2, 1 +5t3) object that moves from (1,1, 1) to (4,5,6) along the curve