Purchase Solution

Second Order Differential Equation - Power Series Solution

Not what you're looking for?

Ask Custom Question

Hi there, I have a question regarding Differential Equations which can be located here http://none-questions.blogspot.com/2011/09/d-q7.html. can someone please take a look? Thanks.

Purchase this Solution

Solution Summary

We solve a given second order ordinary differential equation by deriving and solving a recurrence in the power series of the solution.

Solution Preview

We wish to solve the following differential equation using power series:

xy'' - 2y + 9x^5 y = 0.

First write out y(x) as a power series, i.e.

y(x) = sum_{k=0}^infty(c_k x^k).

Then we have

y'(x) = sum_{k=1}^infty[k c_k x^(k-1)]
and

y''(x) = sum_{k=2}^infty[k(k-1) c_k x^(k-2)]

whence

0 = xy'' - 2y + 9x^5 y
= sum_{k=2}^infty[k(k-1) c_k x^(k-1)] - 2 ...

Purchase this Solution


Free BrainMass Quizzes
Graphs and Functions

This quiz helps you easily identify a function and test your understanding of ranges, domains , function inverses and transformations.

Solving quadratic inequalities

This quiz test you on how well you are familiar with solving quadratic inequalities.

Geometry - Real Life Application Problems

Understanding of how geometry applies to in real-world contexts

Know Your Linear Equations

Each question is a choice-summary multiple choice question that will present you with a linear equation and then make 4 statements about that equation. You must determine which of the 4 statements are true (if any) in regards to the equation.

Multiplying Complex Numbers

This is a short quiz to check your understanding of multiplication of complex numbers in rectangular form.