52.1.15 problem 13

Internal problem ID [8232]
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. Section 6.2 SOLUTIONS ABOUT ORDINARY POINTS. EXERCISES 6.2. Page 246
Problem number : 13
Date solved : Monday, January 27, 2025 at 03:46:33 PM
CAS classification : [[_2nd_order, _missing_y]]

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

Using series method with expansion around

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

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 46

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

\[ y = y \left (0\right )+\left (x +\frac {1}{2} x^{2}+\frac {1}{3} x^{3}+\frac {1}{4} x^{4}+\frac {1}{5} x^{5}+\frac {1}{6} x^{6}+\frac {1}{7} x^{7}\right ) y^{\prime }\left (0\right )+O\left (x^{8}\right ) \]

✓ Solution by Mathematica

Time used: 0.002 (sec). Leaf size: 53

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

\[ y(x)\to c_2 \left (\frac {x^7}{7}+\frac {x^6}{6}+\frac {x^5}{5}+\frac {x^4}{4}+\frac {x^3}{3}+\frac {x^2}{2}+x\right )+c_1 \]