## 17Calculus Differential Equations - Power Series Solution

##### 17Calculus

This page discusses how to solve differential equations using power series. This is also called Frobenius Method.

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

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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