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Solving Differential Equations is not always a trivial matter. As you have seen thus far some techniques are more fruitful than others due to the internal structure with a given differential equation. In this section, you will be presented with a “powerful” procedure for solving differential equations using power series. 

A(x)=\displaystyle\sum_{n=0}^{\infty}a_nx^n

To employ this technique you may wish to review some commonly used Power Series

Practice Problems

Determine the power series solutions for the given problems. 

  1. \displaystyle (x^2-1)y”+xy’-y=0
  2. \displaystyle (x^2+2)y”+3xy’-y=0
  1. \displaystyle y”-(x+1)y’-y=0
  2. \displaystyle (x-1)y”+y’=0=0
  1. \displaystyle (x+2)y”+xy’-y=0
  2. \displaystyle (x-1)y”-xy’+y=0

Virtual Lessons

Need some additional help understanding how to apply this technique? Click Here to visit the virtual lesson section.