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QUESTION 9 Letr and r2 be two indicial roots of the differential equation 2x(x - 1)y"-(x...
(1 point) Consider the differential equation 2x(x )y"3 - 1)y -y0 which has a regular singular...
(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...
12. All the roots of the indicial equation of the following differential equation are: * (8...
12. All the roots of the indicial equation of the following differential equation are: * (8 Puan) x?y" + xy' + (x - 1)y = 0 O 0, 1, -1 O and -1 0 and 1 0 1 and -1 none of these
12. All the roots of the indicial equation of the following differential equation are: (8 Puan)...
12. All the roots of the indicial equation of the following differential equation are: (8 Puan) By + xy + (x-1)y = 0 O and 1 none of these O and -1 0, 1, -1 0 1 and - 1
5. (20 pts) For the differential equation: sume the following information (you don't need to show this). e roots of the indicial equation are ri 4 and 2--2. In addition, after substituting y...
5. (20 pts) For the differential equation: sume the following information (you don't need to show this). e roots of the indicial equation are ri 4 and 2--2. In addition, after substituting y t and its derivatives into the differential equation and reindexing we get: Given this information, find all Frobenius solutions for x >0. Make sure you include the "nth" term in your solution(s). If a solution does not exist for an exponent, show why.
5. (20 pts) For...
Problem 11 Previous Problem Problem List Next Problem (1 point) Consider the differential equation 2x(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 +...
Question 3 Consider the ordinary differential equation (ODE) 2xy" + (1 + x)y' + 3y =...
Question 3 Consider the ordinary differential equation (ODE) 2xy" + (1 + x)y' + 3y = 0, in the neighbourhood of the origin. a) Show that x = 0 is a regular singular point of the ODE. (10) b) By seeking an appropriate solution to the ODE, show that G=- (10) i) the roots to the indicial equation of the ODE are 0 and 1/2. [10] ii) the recurrence formula used to determine the power series coefficients, ens when one...
(a) 5. Make up a differential equation that will have as the roots of its indicial...
(a)
5. Make up a differential equation that will have as the roots of its indicial equation (a) 1,4 (b) 3,3 (c) 1/2,2 (d) -1/2,1/2
6: Problem 4 Previous Problem List Next (1 point) Consider the differential equation which has a ...
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...
Consider the differential equation (a) Find ri, r2, roots of the characteristic polynomial of the equation...
Consider the differential equation (a) Find ri, r2, roots of the characteristic polynomial of the equation above. T1,T2 (b) Find a set of real-valued fundamental solutions to the homogeneous differential equation corresponding to the one above. n(t) = v2(t) (c) Find a particular solution yp of the differential equation above. Bplt)
Consider the differential equation y" + 8y' + 15 y=0. (a) Find r1 r2, roots of...
Consider the differential equation y" + 8y' + 15 y=0. (a) Find r1 r2, roots of the characteristic polynomial of the equation above. = 11, 12 M (b) Find a set of real-valued fundamental solutions to the differential equation above. yı(t) M y2(t) M (C) Find the solution y of the the differential equation above that satisfies the initial conditions y(0) = 4, y(0) = -3. g(t) = M (10 points) Solve the initial value problem y" - 54' +...
(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...
12. All the roots of the indicial equation of the following differential equation are: * (8 Puan) x?y" + xy' + (x - 1)y = 0 O 0, 1, -1 O and -1 0 and 1 0 1 and -1 none of these
12. All the roots of the indicial equation of the following differential equation are: (8 Puan) By + xy + (x-1)y = 0 O and 1 none of these O and -1 0, 1, -1 0 1 and - 1
5. (20 pts) For the differential equation: sume the following information (you don't need to show this). e roots of the indicial equation are ri 4 and 2--2. In addition, after substituting y t and its derivatives into the differential equation and reindexing we get: Given this information, find all Frobenius solutions for x >0. Make sure you include the "nth" term in your solution(s). If a solution does not exist for an exponent, show why.
5. (20 pts) For...
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 +...
Question 3 Consider the ordinary differential equation (ODE) 2xy" + (1 + x)y' + 3y = 0, in the neighbourhood of the origin. a) Show that x = 0 is a regular singular point of the ODE. (10) b) By seeking an appropriate solution to the ODE, show that G=- (10) i) the roots to the indicial equation of the ODE are 0 and 1/2. [10] ii) the recurrence formula used to determine the power series coefficients, ens when one...
(a)
5. Make up a differential equation that will have as the roots of its indicial equation (a) 1,4 (b) 3,3 (c) 1/2,2 (d) -1/2,1/2
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...
Consider the differential equation (a) Find ri, r2, roots of the characteristic polynomial of the equation above. T1,T2 (b) Find a set of real-valued fundamental solutions to the homogeneous differential equation corresponding to the one above. n(t) = v2(t) (c) Find a particular solution yp of the differential equation above. Bplt)
Consider the differential equation y" + 8y' + 15 y=0. (a) Find r1 r2, roots of the characteristic polynomial of the equation above. = 11, 12 M (b) Find a set of real-valued fundamental solutions to the differential equation above. yı(t) M y2(t) M (C) Find the solution y of the the differential equation above that satisfies the initial conditions y(0) = 4, y(0) = -3. g(t) = M (10 points) Solve the initial value problem y" - 54' +...
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