Verify by direct substitution that the given power series is a solution of the indicated differential equation.
31.y =[infinity]∑ n = 0 to x (- 1) ⁿ/(n!) × x²ⁿ, y' + 2xy = 0
32.y = [infinity]∑n = 0 to x (- 1) ⁿ x²ⁿ (1 + x ²) y'+2xy=0
33.y =[infinity]∑n = 1 to r ((- 1) ⁿ⁺¹) /n x ⁿ (x + 1) yⁿ +y' =0
34.y =[infinity]∑n = 0 to x (- 1) ⁿ/(2²ⁿ(n!) ²) x²ⁿ, xyⁿ + y' + xy = 0