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 |
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To get started, here is a great video explaining under what conditions we can use power series to solve differential equations.
video by Trefor Bazett |
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Here is a great video with a step-by-step explanation on how to solve these problems, including an example.
video by Dr Chris Tisdell |
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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
video by PatrickJMT |
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Solve \( y' + 2xy = 0 \)
Problem Statement
Solve \( y' + 2xy = 0 \)
Solution
video by blackpenredpen |
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Solve \( y'' + y = 0 \)
Problem Statement
Solve \( y'' + y = 0 \)
Solution
video by PatrickJMT |
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Solve \( y'' - xy = 0 \)
Problem Statement
Solve \( y'' - xy = 0 \)
Solution
video by Houston Math Prep |
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Solve \( y'' - 2xy' + y = 0 \)
Problem Statement
Solve \( y'' - 2xy' + y = 0 \)
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
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Really UNDERSTAND Differential Equations
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