Internal problem ID [11894]
Book: Differential Equations by Shepley L. Ross. Third edition. John Willey. New Delhi.
2004.
Section: Chapter 6, Series solutions of linear differential equations. Section 6.1. Exercises page
232
Problem number: 11.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _exact, _linear, _homogeneous]]
\[ \boxed {y^{\prime \prime }-y^{\prime } x -y=0} \] With initial conditions \begin {align*} [y \left (0\right ) = 1, y^{\prime }\left (0\right ) = 0] \end {align*}
With the expansion point for the power series method at \(x = 0\).
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 14
Order:=6; dsolve([diff(y(x),x$2)-x*diff(y(x),x)-y(x)=0,y(0) = 1, D(y)(0) = 0],y(x),type='series',x=0);
\[ y \left (x \right ) = 1+\frac {1}{2} x^{2}+\frac {1}{8} x^{4}+\operatorname {O}\left (x^{6}\right ) \]
✓ Solution by Mathematica
Time used: 0.001 (sec). Leaf size: 19
AsymptoticDSolveValue[{y''[x]-x*y'[x]-y[x]==0,{y[0]==1,y'[0]==0}},y[x],{x,0,5}]
\[ y(x)\to \frac {x^4}{8}+\frac {x^2}{2}+1 \]