QuestionUse the power series to solve the following Differential Equation up to its indicial equation $$x \frac{d^{2} y}{d x^{2}}+\frac{d y}{d x}+x^{2} y=0$$ (6 marks)

Studdy Solution
Derive the indicial equation from the lowest power of $x$:
The indicial equation is derived from the lowest power of $x$, which is when $m = 0$:
$$a_1 = 0$$
This implies that the indicial equation is trivial in this case, as the lowest power does not provide a non-zero condition.
The indicial equation is trivial, indicating no additional conditions from the lowest power of $x$.