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1) Find the first 5-term in the power series general solution to the DE: Y" –...
Find the general solution of y" + xy' + 2y = 0 in terms of power series in x. State the radius of convergence of the series.
Find the first five terms of the series solution to the IVP (y +(1-2) +2y=e", y(0) = -5, (y0 =1, by making use of the general power series representation in (2). Hint: Recall the Taylor/power series for et about the point 0.
4. Show that ΣΕǐrk is a solution to y" +/-2-0. (a) Find the general series solution to the DE 2rzy"-ry'+ +1-0 on (0.0c) 5. alouut. the regular singular point ! =0. (b) Consider your answer to part (a) and explain whether your series solutions will be Dower series or not. 4. Show that ΣΕǐrk is a solution to y" +/-2-0. (a) Find the general series solution to the DE 2rzy"-ry'+ +1-0 on (0.0c) 5. alouut. the regular singular point !...
2. Find the first three nonzero terms in a power series expansion about to = 0 of the solution of the initial value problem y" - xy + 2y = 0, y(0) = 0,7'0) = 1. Hint: Compute up to 25.
2. Find two power series solutions and give the general solution about the ordinary point i = 0. It is suffeient to find the first four nonzero terms of each solution. Continue on the next page if necessary. y" + xy = 0
3. Find the first three nonzero terms in a power series expansion about to 1 of the general solution of the differential equation xy + y = 0. Hint: Compute up to a2.
(10) Find the first six non-zero terms of the power series solution of the following problem about the ordinary point zo = 0 (That is, find the first three non-zero terms for yı and find the first three non-zero terms for y2, where the general solution is y = Ciyi + c2y2): + 20 + 2y = 0
Use the power series method to find the general solution near x = 0 of (x2 + 4)y" + xy = x + 2.
3. Find the general solution to the differential equation y"2y 0 as a power series about 0 involving two free constants; the formula for the nth coefficient need not be in 'simplified' form.
In this exercise we consider finding the first five coefficients in the series solution of the first order linear initial value problem (+3)y' 2y 0 subject to the initial condition y(0) 1. Since the equation has an ordinary point at z 0 it has a power series solution in the form We learned how to easily solve problems like this separation of variables but here we want to consider the power series method (1) Insert the formal power series into...