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Question 1 4 pts To find a power series solution about x = 0 to y...
Find the indicated coefficients of the power series solution about x=0 of the differential equation. (x^2+1)y''-xy'+y=0, y(0)=3, y'(0)=-6 (1 point) Find the indicated coefficients of the power series solution about 0 of the differential equation (x2 1)y ry y 0, (0) 3, y' (0) -6 r2 24+ r(9) (1 point) Find the indicated coefficients of the power series solution about 0 of the differential equation (x2 1)y ry y 0, (0) 3, y' (0) -6 r2 24+ r(9)
(1 point) Find the indicated coefficients of the power series solution about x-0 of the differential equation (x2-x+1y"-y-3y = 0, y(0) = 0, y(o) =-8 x2+ 4 (1 point) Find the indicated coefficients of the power series solution about x-0 of the differential equation (x2-x+1y"-y-3y = 0, y(0) = 0, y(o) =-8 x2+ 4
4. (a) Solve the differential equation (1 − x 2 )y ′′ − 2xy′ + λ(λ + 1)y = 0 using power series centered at 0 , in which λ is a constant. Write your solution as a linear combination of two independent solutions whose coefficients are expressed in terms of λ . Compute the coefficients of each solution up to and including the x 5 term. Without computing them, what is the smallest possible value of the radius of...
4. (a) Solve the differential equation (1 − x 2 )y ′′ − 2xy′ + λ(λ + 1)y = 0 using power series centered at 0 , in which λ is a constant. Write your solution as a linear combination of two independent solutions whose coefficients are expressed in terms of λ . Compute the coefficients of each solution up to and including the x 5 term. Without computing them, what is the smallest possible value of the radius of...
Question 8 3 pts The power series solution of the Initial-Value Problem (IVP) (x2 + 1)yll + xyl + 2xy = 0 y(0) = 2 is given by y (0) = 3 23 3x5 = 2 1 + + ...)+(2-* + + ...) + 3 20 None of them 7x3 21.25 y= 2 + 3x + +... 6 2 4 --- 3(-one -+...) +2(1-**+..) 7274 y= 2 + x + +...
(1) Sok power series solution of the forma y(z)-Σ-oanz" to the differential equation: (a) (3 pts) Find recurrence relations for the coefficents, an (b) (4 pts) Use the recurrence relation to give the first three, n-zero terms of the power series solution to the initial value problem: y'-2xy = z, y(0) = 2 (c) (1 pt) Identify the solution as a common function (in closed form). (1) Sok power series solution of the forma y(z)-Σ-oanz" to the differential equation: (a)...
Consider the ODE:3xy"+y' - 2xy = 0. Find the general solution in power series form about the regular singular point x = 0, following parts (a) – (c), below. (a) Obtain the recurrence relation. (b) Find the exponents of the singularity. (e) Obtain only one of the two linearly independent solutions, call it y(x), that corresponds to the smaller exponent of the singularity; but, only explicitly include the first four non-zero terms of the power series solution. Write down the...
= 0 of the differential equation (1 point) Find the indicated coefficients of the power series solution about r y" - (sin )y=cos y(0) 3, y'(0)-4 +0(*) y=3-4 = 0 of the differential equation (1 point) Find the indicated coefficients of the power series solution about r y" - (sin )y=cos y(0) 3, y'(0)-4 +0(*) y=3-4
(1 point) Find the indicated coefficients of the power series solution about x = 0 of the differential equation -(sinx)y y(0) = -5, y'(0) = 3 = cos x, x2 y 53x (1 point) Find the indicated coefficients of the power series solution about x = 0 of the differential equation -(sinx)y y(0) = -5, y'(0) = 3 = cos x, x2 y 53x
Question 7 3 pts The solution of the Initial-Value Problem (IVP) zy! - 2y = 4(x - 2) y(1) = 4 y (1) = -1 is 1 23 +22 -3 +3 +2.3 -2.0.4 1 Y L 22 - 2.0 + 4 2 None of them 0 4 2.- - 2 + 1 y = 2 Question 8 3 pts The power series solution of the Initial-Value Problem (IVP) (22 +1)yll + xy + 2xy = 0 y(0) = 2 is...