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Differential Equations2D

Series Solutions - Theory & Concepts

Using power series methods, including Radius of Convergence and the Frobenius Method, to solve differential equations with variable coefficients.

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Power Series Solution

Solving $y' = y$ with $y(0)=1$ around the ordinary point $x_0=0$ .

y(x) \approx \sum_{n=0}^{0} \frac{x^n}{n!}

Notice how adding more terms increases the interval where the polynomial approximation closely matches the exact exponential solution.

Number of Terms (

N

)1

LinearDegree 9

Exact Solution

e^x

Series Approximation

x ∈ [-3, 3]

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