52.2.11 problem 11

Internal problem ID [8262]
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. 6.3 SOLUTIONS ABOUT SINGULAR POINTS. EXERCISES 6.3. Page 255
Problem number : 11
Date solved : Monday, January 27, 2025 at 03:47:20 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} \left (x^{2}-1\right ) y^{\prime \prime }+5 \left (1+x \right ) y^{\prime }+\left (x^{2}-x \right ) y&=0 \end{align*}

Using series method with expansion around

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

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 74

Order:=8; 
dsolve((x^2-1)*diff(y(x),x$2)+5*(x+1)*diff(y(x),x)+(x^2-x)*y(x)=0,y(x),type='series',x=0);
 

\[ y = \left (1-\frac {1}{6} x^{3}-\frac {1}{8} x^{4}-\frac {3}{10} x^{5}-\frac {17}{45} x^{6}-\frac {199}{336} x^{7}\right ) y \left (0\right )+\left (x +\frac {5}{2} x^{2}+5 x^{3}+\frac {26}{3} x^{4}+\frac {1661}{120} x^{5}+\frac {4967}{240} x^{6}+\frac {14881}{504} x^{7}\right ) y^{\prime }\left (0\right )+O\left (x^{8}\right ) \]

✓ Solution by Mathematica

Time used: 0.003 (sec). Leaf size: 89

AsymptoticDSolveValue[(x^2-1)*D[y[x],{x,2}]+5*(x+1)*D[y[x],x]+(x^2-x)*y[x]==0,y[x],{x,0,"8"-1}]
 

\[ y(x)\to c_1 \left (-\frac {199 x^7}{336}-\frac {17 x^6}{45}-\frac {3 x^5}{10}-\frac {x^4}{8}-\frac {x^3}{6}+1\right )+c_2 \left (\frac {14881 x^7}{504}+\frac {4967 x^6}{240}+\frac {1661 x^5}{120}+\frac {26 x^4}{3}+5 x^3+\frac {5 x^2}{2}+x\right ) \]