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

In summary, the conversation discusses a differential equation and its solution, as well as methods for solving series equations and the initial conditions for this particular equation. It also mentions that the equation can be solved analytically and has real-world applications in modeling physical phenomena.
  • #1
angelas
8
0
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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  • #2
Sure, what have you got so far?
 
  • #3
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.
 
  • #4
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.
 

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

What is the solution to the given differential equation?

The solution to the differential equation is y(x) = 2x + sin(x) - 1.

How do you solve a series equation?

To solve a series equation, you must first determine the order of the series, then use algebraic manipulation and/or integration techniques to isolate the variable of interest.

What are the initial conditions for this equation?

The initial conditions for this equation are y(0)=1 and y'(0)=1.

Can this equation be solved analytically?

Yes, this equation can be solved analytically using algebraic manipulation and integration techniques.

What are some real-world applications of this type of equation?

Series equations can be used to model various physical phenomena such as population growth, heat transfer, and chemical reactions.

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