Internal problem ID [4918]
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.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {\left (x -1\right )^{2} y^{\prime \prime }-\left (x -1\right ) y^{\prime }-35 y=0} \end {gather*} With the expansion point for the power series method at \(x = 0\).
✓ Solution by Maple
Time used: 0.003 (sec). Leaf size: 54
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);
\[ y \relax (x ) = \left (1+\frac {35}{2} x^{2}+\frac {35}{6} x^{3}+\frac {665}{12} x^{4}+\frac {259}{4} x^{5}\right ) y \relax (0)+\left (x -\frac {1}{2} x^{2}+\frac {35}{6} x^{3}+\frac {35}{12} x^{4}+\frac {49}{4} x^{5}\right ) D\relax (y )\relax (0)+O\left (x^{6}\right ) \]
✓ Solution by Mathematica
Time used: 0.001 (sec). Leaf size: 70
AsymptoticDSolveValue[(x-1)^2*y''[x]-(x-1)*y'[x]-35*y[x]==0,y[x],{x,0,5}]
\[ y(x)\to c_1 \left (\frac {259 x^5}{4}+\frac {665 x^4}{12}+\frac {35 x^3}{6}+\frac {35 x^2}{2}+1\right )+c_2 \left (\frac {49 x^5}{4}+\frac {35 x^4}{12}+\frac {35 x^3}{6}-\frac {x^2}{2}+x\right ) \]