Solve Series Equation: xy+(sinx)y'+2xy=3x^2, y(0)=y'(0)=1

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Homework Help Overview

The problem involves solving a differential equation of the form xy'' + (sin x)y' + 2xy = 3x^2, with initial conditions y(0) = y'(0) = 1. The context is centered around series solutions in the realm of differential equations.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss the possibility of using a series solution, noting that 0 is an ordinary point. There is uncertainty regarding how to handle the term sin x within the series framework.

Discussion Status

The discussion is ongoing, with participants exploring the formulation of the series solution and the implications of the sin x term. Some guidance has been offered regarding the need to express sin x as a series for coefficient comparison.

Contextual Notes

There is a focus on the initial conditions provided and the challenge of incorporating the sin x term into the series solution approach.

angelas
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Hi everyone,
Can anyone help me find the solution of this equation using series?

xy"+(sinx)y'+2xy=3x^2
y(0)=y'(0)=1

Thanks in advance
 
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Sure, what have you got so far?
 
Galileo said:
Sure, what have you got so far?

I know that 0 is an ordinary point and therefore I can write the solution in form of series. But I don't know what to do with sin x.
 
If you assume a series solution you have to compare coefficients later on, so it would help if sin x is written as a series.
 

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