In Exercises 1–12 find the coefficients a0,. . . , aN for N at least 7 in the series solution y = SUM∞ n=0 anx n of the initial value problem.
1. (1 + 3x)y" + xy' + 2y = 0, y(0) = 2, y0 (0) = −3
7. (4 + x)y''+ (2 + x)y' + 2y = 0, y(0) = 2, y0 (0) = 5
Please help with both, thank you!
In Exercises 1–12 find the coefficients a0,. . . , aN for N at least 7 in the series solution y = SUM∞ n=0 anx n of the...
Differential Equation: Series Solutions Near an Ordinary point,
find a0 to a7 in the power series for the solution of the
IVP.
In Exercises 19-28 find the coefficients ao. an for N at least 7 in the series solution n=0 of the initial value problem. Take xo to be the point where the initial conditions are imposed
In Exercises 19-28 find the coefficients ao. an for N at least 7 in the series solution n=0 of the initial value problem....
11: Find formulas for an, the coefficients for the power series solution of the initial value problem below. Then use the initial conditions to find the first four nonzero coefficients. y" – (x - 2)y' + 2y = 0, y(0) = 2, y'(0) = -1
Question 8 (10 marks) Solve the following initial value problem by means of a power series about the ordinary point x=0 y" + 3x?y' + xy = 0, y0)=2, y0) - 6 Find the recurrence relation for the coefficients, and also find the first five non-zero terms of the power series solution
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)
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...
y"-xy,-у 0, find the recurrence relation for the coefficients of the r series solution aboutx 0. Then find the first six nonzero terms of the particular solution that satisfies y(0) = 1 and y'(0) = 2.
Question 9
In Exercises 7–11 solve the initial value problem. 7. y' – 2y = xy3, y(0) = 2/2 8. y' – xy = xy3/2, y(1) = 4 9. xy' + y = x4y4, y(1) = 1/2 10. y' – 2y = 2y1/2, y(0) = 1 11. y' – 4y = 402, y(0) = 1
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.
evens from 2 and 6
In Exercises 1-6 find a particular solution by the method used in Example 5.3.2. Then find the general solution and, where indicated, solve the initial value problem and graph the solution. 1. y' + 5y - 6y= 22 + 180 - 1842 2. y' - 4y + 5y = 1+ 5.0 3. y' + 8y + 7y = -8-2+24x2 + 7ar3 4. y' - 4y + 4y = 2 + 8x - 4.2 CIG /'...
2a,2b, and 2c
1. Assuming x > 0, find the general solution of the following Euler equa- tions. f) 5x2y" +12xy' +2y = 0 g) 2y"xy 0 h) a2y" - 2xy =0 i) a2y"-ay-n(n + 2)y 0, where n is a positive integer a) x2y"-3ay 4y 0 b) x2y"-5ay +10y 0 c) 6x2y" +7xy - y 0 d) xy"y0 e) x2y"-3ay' +13y 0 2. Find the solution of the following problems. Before doing these prob- lems, you might want to...