Diff EqPower Series

Power Series Solution of ODEs

Solve y″+P(x)y′+Q(x)y=0 around an ordinary point using y=Σaₙxⁿ. Derive recurrence relations and plot partial sums.

Live Calculator · Step-by-Step · Differential Equations

ODE Selection

ODE — y″+P(x)y′+Q(x)y=0

Number of terms N (2–8)

Results

ODE

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Recurrence Relation

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Series y₁(x) (a₀=1, a₁=0)

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Series y₂(x) (a₀=0, a₁=1)

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Step-by-Step Work

Select an ODE and compute.

Partial sum y₁(x) vs exact (blue=series, purple=exact)

Put It Into Practice

The calculator shows the steps — a quiz proves you can do them on your own.

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