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17Calculus Differential Equations - Power Series Solution

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Single Variable Calculus
Derivatives
Integrals
Multi-Variable Calculus
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This page discusses how to solve differential equations using power series. This is also called Frobenius Method.

Topics You Need To Understand For This Page

power series basics of differential equations

To get started, here is a great video explaining under what conditions we can use power series to solve differential equations.

Trefor Bazett - When can you use Series to solve ODEs? Ordinary vs Singular Points

video by Trefor Bazett

Here is a great video with a step-by-step explanation on how to solve these problems, including an example.

Dr Chris Tisdell - Power series solution to differential equations: a tutorial

video by Dr Chris Tisdell

Ordinary Differential Equations (Dover Books on Mathematics)

Practice

Unless otherwise instructed, solve the following differential equations using power series. If initial conditions are given, determine the particular solution.

Solve \( y' - y = 0 \)

Problem Statement

Solve \( y' - y = 0 \)

Solution

PatrickJMT - 2610 video solution

video by PatrickJMT

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Solve \( y' + 2xy = 0 \)

Problem Statement

Solve \( y' + 2xy = 0 \)

Solution

blackpenredpen - 2612 video solution

video by blackpenredpen

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Solve \( y'' + y = 0 \)

Problem Statement

Solve \( y'' + y = 0 \)

Solution

PatrickJMT - 2611 video solution

video by PatrickJMT

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Solve \( y'' - xy = 0 \)

Problem Statement

Solve \( y'' - xy = 0 \)

Solution

Houston Math Prep - 2609 video solution

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Solve \( y'' - 2xy' + y = 0 \)

Problem Statement

Solve \( y'' - 2xy' + y = 0 \)

Solution

blackpenredpen - 2608 video solution

video by blackpenredpen

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Solve \( y'' - 2y' + y = x; ~~~ y(0)=0, y'(0) = 1 \)

Problem Statement

Solve \( y'' - 2y' + y = x; ~~~ y(0)=0, y'(0) = 1 \)

Solution

2613 video solution

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Really UNDERSTAND Differential Equations

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Practice Instructions

Unless otherwise instructed, solve the following differential equations using power series. If initial conditions are given, determine the particular solution.

Do NOT follow this link or you will be banned from the site!

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