Online Math Tutor LLC

Discover the Path to Mathematical Mastery 
An Education That Counts

Online Math Tutor LLC

Discover the Path to Mathematical Mastery 
An Education That Counts

Practice Problems: Separable DEs

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. 

Find two power series solutions for the given differential equation about the ordinary point \(x=0\). 

  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. \(\displaystyle (x-1)y”-xy’+y=0\)

Use the Frobenius method to obtain two linearly independent series solutions about \(x=0\).

  1. \(\displaystyle 2xy”-y’+2y=0\)
  2. \(\displaystyle 2xy”+5y’+xy=0\)
  1. \(\displaystyle 2x^2y”-xy’+(x^2+1)y=0\)
  2. \(\displaystyle 2xy”-(3+2x)y’+y=0\)
  1. \(\displaystyle 9x^2y”+9x^2y’+2y=0\)
  2. \(\displaystyle 2x^2y”+3xy’+(2x-1)y=0\)

Virtual Lessons

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