46.5.3 problem 13

Internal problem ID [7339]
Book : ADVANCED ENGINEERING MATHEMATICS. ERWIN KREYSZIG, HERBERT KREYSZIG, EDWARD J. NORMINTON. 10th edition. John Wiley USA. 2011
Section : Chapter 5. Series Solutions of ODEs. REVIEW QUESTIONS. page 201
Problem number : 13
Date solved : Monday, January 27, 2025 at 02:50:40 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} \left (x -1\right )^{2} y^{\prime \prime }-\left (x -1\right ) y^{\prime }-35 y&=0 \end{align*}

Using series method with expansion around

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

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 59

Order:=6; 
dsolve((x-1)^2*diff(y(x),x$2)-(x-1)*diff(y(x),x)-35*y(x)=0,y(x),type='series',x=0);
 

\[ y = \left (1+\frac {35}{2} x^{2}+\frac {35}{6} x^{3}+\frac {665}{12} x^{4}+\frac {259}{4} x^{5}\right ) y \left (0\right )+\left (x -\frac {1}{2} x^{2}+\frac {35}{6} x^{3}+\frac {35}{12} x^{4}+\frac {49}{4} x^{5}\right ) y^{\prime }\left (0\right )+O\left (x^{6}\right ) \]

✓ Solution by Mathematica

Time used: 0.002 (sec). Leaf size: 70

AsymptoticDSolveValue[(x-1)^2*D[y[x],{x,2}]-(x-1)*D[y[x],x]-35*y[x]==0,y[x],{x,0,"6"-1}]
 

\[ y(x)\to c_1 \left (\frac {259 x^5}{4}+\frac {665 x^4}{12}+\frac {35 x^3}{6}+\frac {35 x^2}{2}+1\right )+c_2 \left (\frac {49 x^5}{4}+\frac {35 x^4}{12}+\frac {35 x^3}{6}-\frac {x^2}{2}+x\right ) \]