Use the power series method to find the general solution near x = 0 of (x2...
6 (1) Use power-series to find the general solution near x 0 of: dax +b(ab)) -( (ii) Use initial conditions: u(0) = c and (u))(0) = d ) My problem: (aa-(IX) +n))st (9))(v)-0 () My initial conditions( 5 and)0)7 to determine the unknown constants. 6 (1) Use power-series to find the general solution near x 0 of: dax +b(ab)) -( (ii) Use initial conditions: u(0) = c and (u))(0) = d ) My problem: (aa-(IX) +n))st (9))(v)-0 () My initial...
Use the Frobenius method to find the general solution near x = 0 of the hypergeometric equation x(1 - x)y" + [C - (A + B +1)x]y' - ABy = 0 where A and B are any real numbers, and C is any real nonintegral number.
Differential Equations Series Solutions Near a Ordinary Point find the power series in x for the general solution (1+x^2)y"+2xy-2y=0
2. Solve each of these ODEs using power series method expanded around Xo = 0. Find the recurrence relation and use it to find the first FOUR terms in each of the two linearly independent solution. Express your answer in general form where possible (well, it is not always possible). (a) (25 marks) (x2 + 2)y” - xy + 4y = 2x - 1-47 Note: expressa in terms of power series. (b) 2x2y" + 3xy' + (2x - 1) =...
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)
11. Apply the power series method to find the solution of the differential equation: xy" (x )y ty-0
Find the general solution of y" + xy' + 2y = 0 in terms of power series in x. State the radius of convergence of the series.
= Q4. Use the Frobenius method to find the general solution near x O of the hypergeometric equation X(1 — x)y” + [C – (A + B + 1)x]y' – ABy = 0 where A and B are any real numbers, and C is any real nonintegral number.
(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
Find the first four nonzero terms in a power series expansion about x = 0 for a general solution to the given differential equation.(x2 + 18)y'' + y = 0