64.14.14 problem 14

Internal problem ID [13573]
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
Date solved : Tuesday, January 28, 2025 at 05:53:11 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} \left (2 x^{2}-3\right ) y^{\prime \prime }-2 x y^{\prime }+y&=0 \end{align*}

Using series method with expansion around

\begin{align*} 0 \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=-1\\ y^{\prime }\left (0\right )&=5 \end{align*}

✓ Solution by Maple

Time used: 0.001 (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);
 

\[ y = -1+5 x -\frac {1}{6} x^{2}-\frac {5}{18} x^{3}-\frac {1}{216} x^{4}-\frac {7}{216} x^{5}+\operatorname {O}\left (x^{6}\right ) \]

✓ Solution by Mathematica

Time used: 0.003 (sec). Leaf size: 36

AsymptoticDSolveValue[{(2*x^2-3)*D[y[x],{x,2}]-2*x*D[y[x],x]+y[x]==0,{y[0]==-1,Derivative[1][y][0] ==5}},y[x],{x,0,"6"-1}]
 

\[ y(x)\to -\frac {7 x^5}{216}-\frac {x^4}{216}-\frac {5 x^3}{18}-\frac {x^2}{6}+5 x-1 \]