Internal problem ID [11897]
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: 14.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {\left (2 x^{2}-3\right ) y^{\prime \prime }-2 y^{\prime } x +y=0} \] With initial conditions \begin {align*} [y \left (0\right ) = -1, y^{\prime }\left (0\right ) = 5] \end {align*}
With the expansion point for the power series method at \(x = 0\).
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 20
Order:=6; dsolve([(2*x^2-3)*diff(y(x),x$2)-2*x*diff(y(x),x)+y(x)=0,y(0) = -1, D(y)(0) = 5],y(x),type='series',x=0);
\[ y \left (x \right ) = -1+5 x -\frac {1}{6} x^{2}-\frac {5}{18} x^{3}-\frac {1}{216} x^{4}-\frac {7}{216} x^{5}+\operatorname {O}\left (x^{6}\right ) \]
✓ Solution by Mathematica
Time used: 0.001 (sec). Leaf size: 36
AsymptoticDSolveValue[{(2*x^2-3)*y''[x]-2*x*y'[x]+y[x]==0,{y[0]==-1,y'[0]==5}},y[x],{x,0,5}]
\[ y(x)\to -\frac {7 x^5}{216}-\frac {x^4}{216}-\frac {5 x^3}{18}-\frac {x^2}{6}+5 x-1 \]