Internal problem ID [5024]
Book: Fundamentals of Differential Equations. By Nagle, Saff and Snider. 9th edition. Boston.
Pearson 2018.
Section: Chapter 8, Series solutions of differential equations. Section 8.4. page 449
Problem number: 6.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {\left (x^{3}+1\right ) y^{\prime \prime }-x y^{\prime }+2 y x^{2}=0} \] With the expansion point for the power series method at \(x = 1\).
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 54
Order:=6; dsolve((1+x^3)*diff(y(x),x$2)-x*diff(y(x),x)+2*x^2*y(x)=0,y(x),type='series',x=1);
\[ y \left (x \right ) = \left (1-\frac {\left (x -1\right )^{2}}{2}-\frac {\left (x -1\right )^{3}}{6}+\frac {7 \left (x -1\right )^{4}}{48}+\frac {7 \left (x -1\right )^{5}}{240}\right ) y \left (1\right )+\left (x -1+\frac {\left (x -1\right )^{2}}{4}-\frac {\left (x -1\right )^{3}}{6}-\frac {\left (x -1\right )^{4}}{8}+\frac {\left (x -1\right )^{5}}{12}\right ) D\left (y \right )\left (1\right )+O\left (x^{6}\right ) \]
✓ Solution by Mathematica
Time used: 0.001 (sec). Leaf size: 78
AsymptoticDSolveValue[(1+x^3)*y''[x]-x*y'[x]+2*x*y[x]==0,y[x],{x,1,5}]
\[ y(x)\to c_1 \left (-\frac {1}{20} (x-1)^5+\frac {1}{8} (x-1)^4-\frac {1}{2} (x-1)^2+1\right )+c_2 \left (\frac {19}{240} (x-1)^5-\frac {1}{24} (x-1)^4-\frac {1}{6} (x-1)^3+\frac {1}{4} (x-1)^2+x-1\right ) \]