Practice Problems: Frobenius Method

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

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

\(\displaystyle 2xy”-y’+2y=0\)
\(\displaystyle 2xy”+5y’+xy=0\)

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

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

Virtual Lessons

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

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Practice Problems: Frobenius Method