Problem 2. The following equation is called the LEGENDRE's equation (1-x²)y"-2xy' + Ay=0; where A is a non-negative inte

[answerhappygod]

Problem 2 The Following Equation Is Called The Legendre S Equation 1 X Y 2xy Ay 0 Where A Is A Non Negative Inte 1 (23.5 KiB) Viewed 67 times

Problem 2. The following equation is called the LEGENDRE's equation (1-x²)y"-2xy' + Ay=0; where A is a non-negative integer. a) Show that the recursive formula for the coefficients of the series solution is y(x) = Σc₁a", n=0 Cm+2= m(m+1)-A (m+2)(m+1) Cm b) Show that the radius of convergence of the series with coefficients c₁=1 that coincides the minimum radius of convergence you can determine directly from the equation. c) Find the solution of the given equation if λ=12, and y(0)=0, y'(0)=1. d) Let y(0)=1, y'(0)=0 and A=4. Write down a few terms of the series solution. Use Matlab and draw the numerical solution of the equation and your series solution in the interval [0, 1).