Solve STEP BY STEP using power series about x =
-1,
4(x+1)^2 y'' - 2(x+1)(x+3) y' + (x+4) y = 0.
note, solve by power series, variable transformation
by letting:
w= x+1 = 0
1)Find the power series solution for the equation y'' − y =
x
2)Find the power series solution for the equation y'' + (sinx)y
= x; y(0) = 0; y'(0) = 1
Provide the recurrence relation for the coefficients and derive
at least 3 non-zero terms of the solution.