28.5.7 problem 9.7

Internal problem ID [4594]
Book : Differential equations for engineers by Wei-Chau XIE, Cambridge Press 2010
Section : Chapter 9. Series Solutions of Differential Equations. Problems at page 426
Problem number : 9.7
Date solved : Monday, January 27, 2025 at 09:25:52 AM
CAS classification : [[_2nd_order, _exact, _linear, _homogeneous]]

\begin{align*} \left (x^{2}-1\right ) y^{\prime \prime }+\left (4 x -1\right ) y^{\prime }+2 y&=0 \end{align*}

Using series method with expansion around

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

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 57

Order:=6; 
dsolve((x^2-1)*diff(y(x),x$2)+(4*x-1)*diff(y(x),x)+2*y(x)=0,y(x),type='series',x=0);
 

\[ y \left (x \right ) = \left (1+x^{2}-\frac {1}{3} x^{3}+\frac {13}{12} x^{4}-\frac {11}{20} x^{5}\right ) y \left (0\right )+\left (x -\frac {1}{2} x^{2}+\frac {7}{6} x^{3}-\frac {19}{24} x^{4}+\frac {53}{40} x^{5}\right ) D\left (y \right )\left (0\right )+O\left (x^{6}\right ) \]

✓ Solution by Mathematica

Time used: 0.002 (sec). Leaf size: 66

AsymptoticDSolveValue[(x^2-1)*D[y[x],{x,2}]+(4*x-1)*D[y[x],x]+2*y[x]==0,y[x],{x,0,"6"-1}]
 

\[ y(x)\to c_1 \left (-\frac {11 x^5}{20}+\frac {13 x^4}{12}-\frac {x^3}{3}+x^2+1\right )+c_2 \left (\frac {53 x^5}{40}-\frac {19 x^4}{24}+\frac {7 x^3}{6}-\frac {x^2}{2}+x\right ) \]