3. [8 marks] Consider the differential equation Solve the regular perturbation problem with error...
3. [8 marks] Consider the differential equation Solve the regular perturbation problem with error of order 0(e), ie. up to and including terms of 0(e)
Can someone help show how to answer this question. Thanks in advance. 3. [8 marks] Consider the differential equation d2 dx2 Solve the regular perturbation problem with error of order 0(e2),ie. up to and including terms of 0(e) 3. [8 marks] Consider the differential equation d2 dx2 Solve the regular perturbation problem with error of order 0(e2),ie. up to and including terms of 0(e)
Please show all steps for how to solve this perturbation problem. Thank you. 1. [10 marks] Consider the quadratic equation 2 -0.03x 399 (a) Write this as a perturbation problem. Is it singular or regular? (b) Letting x = ao + aie+ a2e2 + . . . solve up to and including terms of order 0(e2). (c) Compare the solution with the "exact" solution. 1. [10 marks] Consider the quadratic equation 2 -0.03x 399 (a) Write this as a perturbation...
1. [10 marks] Consider the quadratic equation x2-0.03x 3.99. a) Write this as a perturbation problem. Is it sin (b) Letting-ao + aie+ a2ε2 + . . . solve up to and including terms of order 0(e2). (c) Compare the solution with the "exact" solution. 1. [10 marks] Consider the quadratic equation x2-0.03x 3.99. a) Write this as a perturbation problem. Is it sin (b) Letting-ao + aie+ a2ε2 + . . . solve up to and including terms of...
7. Consider the differential equation (a) Show that z 0 is a regular singular point of the above differential equation (b) Let y(x) be a solution of the differential equation, where r R and the series converges for any E (-8,s), s > 0 Substitute the series solution y in to the differential equation and simplify the terms to obtain an expression of the form 1-1 where f(r) is a polynomial of degree 2. (c) Determine the values of r....
6: Problem 4 Previous Problem List Next (1 point) Consider the differential equation which has a regular singular point at x = O. The indicial equation for x = 0 is rt with roots (in increasing order) ri- Find the indicated terms of the following series solutions of the differential equation: (a) y = x,16+ and rE x+ The closed form of solution (a) is y 6: Problem 4 Previous Problem List Next (1 point) Consider the differential equation which...
(1 point) Consider the differential equation 2x(x )y"3 - 1)y -y0 which has a regular singular point atx 0. The indicial equation for x 0 is 2+ 0 r+ with roots (in increasing order) r and r2 Find the indicated terms of the following series solutions of the differential equation: x4. (a) y =x (9+ x+ (b) y x(7+ The closed form of solution (a) is y (1 point) Consider the differential equation 2x(x )y"3 - 1)y -y0 which has...
1 point) Consider the differential equation which has a regular singular point at x = O. The indicial equation for x 0 is r1/2 r+ 0 =0 and r O with roots (in increasing order) r1/2 Find the indicated terms of the following series solutions of the differential equation: (a) y = x, (94 (b)y-x(5+ The closed form of solution (a) is y = xtO r3+ 1 point) Consider the differential equation which has a regular singular point at x...
Problem 11 Previous Problem Problem List Next Problem (1 point) Consider the differential equation 2x(x – 1)y" + 3(x - 1)y' - y = 0 which has a regular singular point at x = 0. The indicial equation for x = 0 is p2 + r+ = 0 with roots (in increasing order) rı = and r2 = Find the indicated terms of the following series solutions of the differential equation: (a) y = x" (3+ x+ x2+ x +...
3. Consider the following differential equation 0o and a series solution to the differential equation of the form a" n-0 (a) Find the recurrence relations for the coefficients of the power series. 3 marks] (b) Determine the radius of convergence of the power series. l mar (c) Write the first eight terms of the series solution with the coefficients written in terms of ao and ai 2 marks] 3. Consider the following differential equation 0o and a series solution to...