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Power Series Solutions for Non-Homogeneous Differential Equations:Y" - Y = x & Y' + Y =e^x

Question Description

I need help with a question. All explanations and answers will be used to help me learn.

Solve using the Power Series Method. Show all Steps. Power Series Solutions for Non-Homogeneous Differential Equations: Y" - Y = x and  the second one is:
 Y' + Y = e^x
These are two different questions. Here is an example of how these questions have to be approached. Here, For Y'' - XY' - 4Y= e^x 

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20130506234449powerseriessolutionsforano

For instance, for n=0       would be:
C_2= 1/(2!) + C_0(4)/(1)(2)       => just plugging 0 for n in this step, and so on. 

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