Solve y''+(1+x^2)y=0 by power series method.

To solve the differential equation \( y'' + (1 + x^2)y = 0 \) using the power series method, we assume a solution of the form:

\[ y = \sum_{n=0}^{\infty} a_n x^n \]

First, we need to find the second derivative of \( y \):

\[ y' = \sum_{n=1}^{\infty} a_n n x^{n-1} \]
\[ y'' = \sum_{n=2}^{\infty} a_n n (n-1) x^{n-2} \]

Now, we substitute \( y \) and \( y'' \)

Learn how to solve the differential equation y'' + (1 + x^2)y = 0 using the power series method. This problem involves using power series expansions to find a solution, suitable for advanced undergraduate students or higher.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation