Use power series to find two linearly independent solutions
centered at the point x=0
1) y'' + 2y' - 2y = 0
2) 2x2y'' + x(x-1)y' - 2y = 0
please show work, thank you!
1.(4-x^2)y''+2y=0, x0=0
(a) Seek power series solutions of the given differential
equation about the given point x0; find the recurrence
relation.
(b) Find the first four terms in each of two solutions y1 and y2
(unless the series terminates sooner)
. (c) By evaluating the Wronskian W(y1, y2)(x0), show that y1
and y2 form a fundamental set of solutions.
(d) If possible, find the general term in each solution.
Power series
Find the particular solution of the differential equation:
(x^2+1)y"+xy'-4y=0 given the boundary conditions x=0, y=1 and y'=1.
Use only the 7th degree term of the solution. Solve for y at x=2.
Write your answer in whole number.