In: Advanced Math
Diff. equations
Consider the equation (x^2 − 2)y''+ 3xy'+ y = 0.
a) Find the general solution as a power series centered at x = 0. Write the first six nonzero terms of the solution. And write the solution using sigma notation with a formula for the coefficients. Write the two linearly independent solutions that form the general solution.
b) Find a power series solution satisfying the initial conditions y(0) = 2 and y' (0) = 3. Write the first six nonzero terms of the solution. And write the solution using sigma notation with a formula for the coefficients.