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Solve the Euler ODE 7. x?y"+ xy'– 9y = x3
9. Solve the IVP with Cauchy-Euler ODE: xy"txy+4y-0; y(1)-o, y )--3 = 0 , use Variat 0 10. Given that y = GXtar2 is a solution of the Cauchy-Euler ODE x, "+ 2xy-2 Parameters to find the general solution of the non-homogeneous ODE y+2xy-y homogeneoury"rQ&)e-ar)-
solve all questions please Question 1 The solution to the ODE y' + 3xy=0 is Question 2 The solution of the IVP Ý – 2y=e*, (0) = 2 is Question 3 The solution to the ODE Y'y=2-3y2 is Question 4 The solution to the ODE XY' – y=-xex
solve the ODE y'+(3/x)(y)=0 , y(1)=5
3. a) Classify each ODE by order and linearity: y" – 3xy' + xy = 0 b) y(4) + 2xy" - x?y' - xy' + sin y = 0 c) 2.5** 12.5x = sint
(8a) Solve the ODE y" - 3y' = 4y (86) Solve the ODE y" - 3y' = 4y + 3 (9a) Solve the ODE" = - 4y (9b) Solve the ODE y" = -4y - 8x
4) xy" + y' – xy = 0,x, = 0 a) What are the points of singularity for each specific problem? b) Does this ODE hold a general power series solution at the specific xO? Justify your answer, if your answer is yes, the proceed as follows: Compute the radius of analyticity and report the corresponding interval, and Identify the recursion formula for the power series coefficient around xo, and write the corresponding solution with at least four non-zero terms...
Starting from the Laguerre ODE xy" + (1 - x) y' + y = 0 a) Obtain the Rodrigues formula for its polynomial solutions Ln(x) b) From the Rodrigues formula, derive the generating function for the Ln(x) given in Table 12.1 (Arfkin,7e)
3)(10 points) Solve the following patially decoupled system. dc de = -xy dy = y - 1
3. Consider the following ODE: (1 + 2%)/" - xy + y = 0 (a) Find the first 3 nonzero terms of the power series expansion (around x = 0) for the general solution. (b) Use the ratio test to determine the radius of convergence of the series. What can you say about the radius of convergence without solving the ODE? (c) Determine the solution that satisfies the initial conditions y(0) = 1 and (0) = 0.