(Solved): Determine the singular points of the given differential equation. \[ \left(x^{2}-1\right) y^{\prime ...

Determine the singular points of the given differential equation. \[ \left(x^{2}-1\right) y^{\prime \prime}+(1-x) y^{\prime}+\left(x^{2}-2 x+1\right) y=0 \] \( x=-1 \) only. All \( x \geq 1 \) All \( x \leq-1 \) There are no singular points. \( x=1 \) and \( x=-1 \) only Find the first four nonzero terms in a power series expansion about \( x_{0}=0 \) for the solution to the given initial value problem: \[ y^{\prime \prime}+(x-2) y^{\prime}-y=0, y(0)=-3, y^{\prime}(0)=0 \] \( -3-\frac{3}{2} x^{2}+x^{3}-\frac{3}{8} x^{4} \) \[ -3-\frac{3}{2} x^{2}+x^{3}+\frac{3}{8} x^{4} \] \( -3-\frac{3}{2} x^{2}-x^{3}-\frac{3}{8} x^{4} \) \( -3-\frac{3}{2} x^{2}-x^{3}+\frac{3}{8} x^{4} \) \( -3+\frac{3}{2} x^{2}-x^{3}+\frac{3}{8} x^{4} \)