Diff EqFrobenius

Frobenius Method — Regular Singular Points

Solve x²y″+xP(x)y′+Q(x)y=0 near a regular singular point using y=xʳΣaₙxⁿ. Find indicial roots and recurrence.

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ODE with Regular Singular Point

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Results

Regular Singular Point

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p₀ = lim x→0 xP(x), q₀ = lim x→0 x²Q(x)

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Indicial Equation & Roots

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First Frobenius Solution y₁

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Second Frobenius Solution y₂

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Step-by-Step Work

Select an ODE and apply Frobenius.

First Frobenius Solution y₁(x) for x∈(0,2]