MathCastle
Differential EquationsEasyFrobenius & Special Functions

Frobenius & Special Functions · Easy problem

Legendre's equation (1−x2)y′′−2xy′+λy=0(1 - x^2)y'' - 2xy' + \lambda y = 0 has a polynomial solution of degree nn exactly when λ=n(n+1)\lambda = n(n+1). For λ=42\lambda = 42, what is the degree of the polynomial solution?