We need at least 10 more requests to produce the answer.
0 / 10 have requested this problem solution
The more requests, the faster the answer.
Consider the equation 3x²y" + x(2 – xy + xy = 0 with regular singular point...
(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...
show that the equation xy"+y'-y=0 has a regular singular point at x=0, find the indicial equation and its roots how many independent solutions does the equation have ?
20. 0/2 points | Previous Answers ZillDiffEQ9 6.3.018 The point x 0 is a regular singular point of the given differential equation. 4x2y"-xy + (x2 + 1)y = 0 Show that the indicial roots r of the singularity do not differ by an integer. (List the indicial roots below as a comma-separated list.) Use the method of Frobenius to obtain two linearly independent series solutions about x-0. Form the general solution on (0, ) 2015 340**. y = C-X1/4 1672...
4. Consider the equation zy" - 2y' y 0 (a) Explain why r 0 is a regular singular point for the given equation (b) Let ri >r2 be two indical roots of the given equation. Using Frobenius' method, find a series solution n(x)-z"Ση_0Cnz". (c) Find the second solution of the form Σ000 bnXntr2 with boメ0, or i (z) Inr +bn+r2 with the first three nonzero terms of the series with coefficient bn 4. Consider the equation zy" - 2y' y...
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...
Given that x =0 is a regular singular point of the given differential equation, show that the indicial roots of the singularity do not differ by an integer. Use the method of Frobenius to obtain two linearly independent series solutions about x = 0. Form the general solution on (0, ∞) 2xy''-y'+y=0
3. [10pts] Consider the DE: xy" + 7xy' + Ty = 0. (a) Find the roots rı and r2 of the indicial equation of the DE (with rı >r2). r = r2 = Solution: (b) If we use Frobenius method to solve the DE, we obtain for the largest indicial root and for n > 0, a recurrence acn relation of the form Cn+1 where a and b are constants. Find a and b. m11
4. Given that x =0 is a regular singular point of the given differential equation, show that the indicial roots of the singularity do not differ by an integer. Use the method of Frobenius to obtain to linearly independent series solutions about x = 0. Form the general solution on (0, 0) kxy” – (2x + 3)y' + y = 0
Consider the differential equation 4x2y′′ − 8x2y′ + (4x2 + 1)y = 0 (a) Verify that x0 = 0 is a regular singular point of the differential equation and then find one solution as a Frobenius series centered at x0 = 0. The indicial equation has a single root with multiplicity two. Therefore the differential equation has only one Frobenius series solution. Write your solution in terms of familiar elementary functions. (b) Use Reduction of Order to find a second...
DETAILS ZILLDIFFEQ9M 6.3.022. MY NOTES The point x = 0 is a regular singular point of the given differential equation. *?y" + xy' + +(x2-3) = 0 Show that the indicial roots r of the singularity do not differ by an integer. (List the indicial roots below as a comma-separated list.) Use the method of Frobenius to obtain two linearly independent series solutions about x = 0. Form the general solution on (0,co). 3 9 9 1 ...) 3328 448...