Initial value problem of ord diff eq

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The discussion centers on solving the initial value problem for the differential equation 3y'' - y' + (x+1)y = 1 with initial conditions y(0) = 0 and y'(0) = 0. The original poster struggles to find a particular solution using familiar methods and considers the power series method as a potential approach. Respondents suggest using series solutions or changing variables to transform the equation into the Airy equation for easier handling. The conversation emphasizes the importance of exploring different solution techniques for complex differential equations. Ultimately, the power series method is recommended as a viable strategy for this problem.
Grothard
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Homework Statement



3y'' -y' + (x+1)y = 1
y(0) = y'(0) = 0


Homework Equations



Not sure, that's the issue


The Attempt at a Solution



I can't quite get this one using the methods I'm familiar with, and I can't guess a particular solution to neither the equation nor the homogenous version thereof. Do I have to use the power series method?
 
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Grothard said:

Homework Statement



3y'' -y' + (x+1)y = 1
y(0) = y'(0) = 0

I can't quite get this one using the methods I'm familiar with, and I can't guess a particular solution to neither the equation nor the homogenous version thereof. Do I have to use the power series method?

Yes, I would expect that.
 
Use series or change variables to reduce it to the Airy equation.
 

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