Internal problem ID [5811]
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.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_y]]
Solve \begin {gather*} \boxed {\left (x -1\right ) y^{\prime \prime }+y^{\prime }=0} \end {gather*} With the expansion point for the power series method at \(x = 0\).
✓ Solution by Maple
Time used: 0.004 (sec). Leaf size: 44
Order:=8; dsolve((x-1)*diff(y(x),x$2)+diff(y(x),x)=0,y(x),type='series',x=0);
\[ y \relax (x ) = y \relax (0)+\left (x +\frac {1}{2} x^{2}+\frac {1}{3} x^{3}+\frac {1}{4} x^{4}+\frac {1}{5} x^{5}+\frac {1}{6} x^{6}+\frac {1}{7} x^{7}\right ) D\relax (y )\relax (0)+O\left (x^{8}\right ) \]
✓ Solution by Mathematica
Time used: 0.001 (sec). Leaf size: 53
AsymptoticDSolveValue[(x-1)*y''[x]+y'[x]==0,y[x],{x,0,7}]
\[ y(x)\to c_2 \left (\frac {x^7}{7}+\frac {x^6}{6}+\frac {x^5}{5}+\frac {x^4}{4}+\frac {x^3}{3}+\frac {x^2}{2}+x\right )+c_1 \]