Internal problem ID [5892]
Book: DIFFERENTIAL EQUATIONS with Boundary Value Problems. DENNIS G. ZILL,
WARREN S. WRIGHT, MICHAEL R. CULLEN. Brooks/Cole. Boston, MA. 2013. 8th
edition.
Section: CHAPTER 6 SERIES SOLUTIONS OF LINEAR EQUATIONS. CHAPTER 6 IN REVIEW.
Page 271
Problem number: 11.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_Emden, _Fowler]]
Solve \begin {gather*} \boxed {\left (x -1\right ) y^{\prime \prime }+3 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: 69
Order:=8; dsolve((x-1)*diff(y(x),x$2)+3*y(x)=0,y(x),type='series',x=0);
\[ y \relax (x ) = \left (1+\frac {3}{2} x^{2}+\frac {1}{2} x^{3}+\frac {5}{8} x^{4}+\frac {9}{20} x^{5}+\frac {29}{80} x^{6}+\frac {163}{560} x^{7}\right ) y \relax (0)+\left (x +\frac {1}{2} x^{3}+\frac {1}{4} x^{4}+\frac {9}{40} x^{5}+\frac {7}{40} x^{6}+\frac {79}{560} x^{7}\right ) D\relax (y )\relax (0)+O\left (x^{8}\right ) \]
✓ Solution by Mathematica
Time used: 0.001 (sec). Leaf size: 91
AsymptoticDSolveValue[(x-1)*y''[x]+3*y[x]==0,y[x],{x,0,7}]
\[ y(x)\to c_2 \left (\frac {79 x^7}{560}+\frac {7 x^6}{40}+\frac {9 x^5}{40}+\frac {x^4}{4}+\frac {x^3}{2}+x\right )+c_1 \left (\frac {163 x^7}{560}+\frac {29 x^6}{80}+\frac {9 x^5}{20}+\frac {5 x^4}{8}+\frac {x^3}{2}+\frac {3 x^2}{2}+1\right ) \]