Determine the recursive relation

Reference no: EM131010866

Consider the following equation: 2xy'' + y' + 3y = 0.

(a) Show that x₀ = 0 is a regular singular point.

(b) Write down the indicial equation and solve it to determine r₁ and r₂, r₁ ≥ r₂.

(c) Let y= _n=0Σ^∞ c_n (r) x^n+r. Determine the recursive relation for c_n(r), i.e., relation between c_n+1(r) and c_n(r).

(d) Take c₀(r) = 1. Find two linearly independent solutions y₁ and y₂ which are valid for x>0 near x₀ =0.

Reference no: EM131010866

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