Find a power series solution to the differential equation, and determine the radius of convergence, (2x-1)y'+2y = 0

Find the first four nonzero terms in a power series expansion of the solution to the given initial value problem. 6y' - 5e²xy=0; y(0) = 1 00 Rewrite the given differential equation in terms of a power series, using a general solution y(x) = Σan (x-xo)". Expand e²x in a power series, writing the first four terms. Select the correct answer below and fill in the answer box to complete your choice. n=0 ∞0 ○ A. 6 Σ n(n-1)a, (x-xo)n-²-5( n=2 00 00 B. 6 Σ n(n-1)an (x-x₁)n-²-5( + ...) Σ na, (x−×。)' n=2 n=1 00 + ...) Σ ªn (x-x₁) = 0 n=0 ∞ 00 ○ c. 6(+) Σ na, (x-xo)n-1-5 Σan (x-xo) n = 0 n=1 n=0 ∞0 + + ... 4 D. 6 6 Σnan (x-x₁)n-1 -5 1+2x+ 2x² + - 3 + ³ + ...). n=1 y(x) = (Type an expression that includes all terms up to order 3.) ¹ = 0 ∞ Σan (x-xo) n = 0 n=0

For the differential equation (x2+1)y'' + (sinx)y' + x4y = 0 what would be the minimum radius of convergence of two linearly independent power series solutions centered at x0=2? (you don't need to find these power series!)