In Problems 25–28, find at least the first four nonzero terms in a power series expansion about \(x=0\) for the solution to the given initial value problem.

\(w^{\prime \prime}+3 x w^{\prime}-w=0\)

\(w(0)=2, w^{\prime}(0)=0\)

Equation Transcription:

Text Transcription:

x=0

w''+3xw'-w=0

w(0)=2, w'(0)=0

Step 1 of 6

We know that

Therefore, it has no singular points which means that is an ordinary point.

Consider a solution of the form:

To substitute in the given equation, we need to find its first and second derivative, with respect to .