Consider the second-order differential equation .
Suppose the method of Frobenius is used to determine a power series solution of this equation. The indicial equation has r = 0 as a double root. So, one of the solutions can be represented as the power series . Assume a₀ ≠ 0.
Assuming that a₀= 1, one solution of the given differential equation is
Assuming that are known, what is the radius of convergence of the power series of the second solution Y₂ (x)?

Question

Consider the second-order differential equation

.
Suppose the method of Frobenius is used to determine a power series solution of this equation. The indicial equation has r = 0 as a double root. So, one of the solutions can be represented as the power series

. Assume a₀ ≠ 0.
Assuming that a₀= 1, one solution of the given differential equation is

Assuming that

are known, what is the radius of convergence of the power series of the second solution Y₂ (x)?

Quizplus · Accepted Answer

The Answer of Consider the second-order differential equation . Suppose the method of Frobenius is used to determine a power series solution of this equation. The indicial equation has r = 0 as a double root. So, one of the solutions can be represented as the power series . Assume a₀ ≠ 0. Assuming that a₀= 1, one solution of the given differential equation is Assuming that are known, what is the radius of convergence of the power series of the second solution Y₂ (x)?

Consider the Second-Order Differential Equation