9. Determine a lower bound for the radius of convergence of the power series solution of the differ- ential equation about the given ordinary point xo. (a) (x² −2x−3)y″ +xy′+4y = 0, (b) (3-1)y"+xy=0, x0 = −2 x0 = 6

5. Given (1 + x²)y" + 2xy' + 4x²y = 0. Without solving the ODE, determine the lower bound for the radius of convergence of the series solution at the center (a) x₁ = 0; (b) x₁ = -1/1.

Find the first four nonzero terms in a power series expansion of the solution to the given initial value problem. (2) (1)-6 = y" - ( cos x)y'-y=0; y[2] = = 3, ... y(x) = (Type an expression that includes all terms up to order 4. Type an exact answer, using as needed.) +...

Find the first four nonzero terms in a power series expansion of the solution to the given initial value problem. y'-3exy=0; y(0) = 2 y(x) = - + ... (Type an expression that includes all terms up to order 3.) ...