Internal problem ID [4494]
Book: Fundamentals of Differential Equations. By Nagle, Saff and Snider. 9th edition. Boston. Pearson
2018.
Section: Chapter 8, Series solutions of differential equations. Section 8.3. page 443
Problem number: 1.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {\left (x +1\right ) y^{\prime \prime }-y^{\prime } x^{2}+3 y=0} \end {gather*} With the expansion point for the power series method at \(x = 0\).
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 49
Order:=6; dsolve((x+1)*diff(y(x),x$2)-x^2*diff(y(x),x)+3*y(x)=0,y(x),type='series',x=0);
\[ y \relax (x ) = \left (1-\frac {3}{2} x^{2}+\frac {1}{2} x^{3}+\frac {1}{8} x^{4}-\frac {3}{10} x^{5}\right ) y \relax (0)+\left (x -\frac {1}{2} x^{3}+\frac {1}{3} x^{4}-\frac {1}{8} x^{5}\right ) D\relax (y )\relax (0)+O\left (x^{6}\right ) \]
✓ Solution by Mathematica
Time used: 0.002 (sec). Leaf size: 63
AsymptoticDSolveValue[(x+1)*y''[x]-x^2*y'[x]+3*y[x]==0,y[x],{x,0,5}]
\[ y(x)\to c_2 \left (-\frac {x^5}{8}+\frac {x^4}{3}-\frac {x^3}{2}+x\right )+c_1 \left (-\frac {3 x^5}{10}+\frac {x^4}{8}+\frac {x^3}{2}-\frac {3 x^2}{2}+1\right ) \]