Internal problem ID [4713]
Book: Schaums Outline Differential Equations, 4th edition. Bronson and Costa. McGraw Hill
2014
Section: Chapter 27. Power series solutions of linear DE with variable coefficients. Supplementary
Problems. page 274
Problem number: Problem 27.39.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {y^{\prime \prime }-y^{\prime } x^{2}-y=0} \end {gather*} With the expansion point for the power series method at \(x = 0\).
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 44
Order:=6; dsolve(diff(y(x),x$2)-x^2*diff(y(x),x)-y(x)=0,y(x),type='series',x=0);
\[ y \relax (x ) = \left (1+\frac {1}{2} x^{2}+\frac {1}{24} x^{4}+\frac {1}{20} x^{5}\right ) y \relax (0)+\left (x +\frac {1}{6} x^{3}+\frac {1}{12} x^{4}+\frac {1}{120} x^{5}\right ) D\relax (y )\relax (0)+O\left (x^{6}\right ) \]
✓ Solution by Mathematica
Time used: 0.001 (sec). Leaf size: 56
AsymptoticDSolveValue[y''[x]-x^2*y'[x]-y[x]==0,y[x],{x,0,5}]
\[ y(x)\to c_2 \left (\frac {x^5}{120}+\frac {x^4}{12}+\frac {x^3}{6}+x\right )+c_1 \left (\frac {x^5}{20}+\frac {x^4}{24}+\frac {x^2}{2}+1\right ) \]