Internal problem ID [5730]
Book: Differential Equations: Theory, Technique, and Practice by George Simmons, Steven Krantz.
McGraw-Hill NY. 2007. 1st Edition.
Section: Chapter 4. Power Series Solutions and Special Functions. Problems for review and discovert.
(A) Drill Exercises . Page 194
Problem number: 1(h).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _exact, _linear, _homogeneous]]
Solve \begin {gather*} \boxed {\left (x -1\right ) y^{\prime \prime }+\left (1+x \right ) y^{\prime }+y=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: 74
Order:=8; dsolve((x-1)*diff(y(x),x$2)+(x+1)*diff(y(x),x)+y(x)=0,y(x),type='series',x=0);
\[ y \relax (x ) = \left (1+\frac {1}{2} x^{2}+\frac {1}{3} x^{3}+\frac {3}{8} x^{4}+\frac {11}{30} x^{5}+\frac {53}{144} x^{6}+\frac {103}{280} x^{7}\right ) y \relax (0)+\left (x +\frac {1}{2} x^{2}+\frac {2}{3} x^{3}+\frac {5}{8} x^{4}+\frac {19}{30} x^{5}+\frac {91}{144} x^{6}+\frac {177}{280} x^{7}\right ) D\relax (y )\relax (0)+O\left (x^{8}\right ) \]
✓ Solution by Mathematica
Time used: 0.001 (sec). Leaf size: 98
AsymptoticDSolveValue[(x-1)*y''[x]+(x+1)*y'[x]+y[x]==0,y[x],{x,0,7}]
\[ y(x)\to c_1 \left (\frac {103 x^7}{280}+\frac {53 x^6}{144}+\frac {11 x^5}{30}+\frac {3 x^4}{8}+\frac {x^3}{3}+\frac {x^2}{2}+1\right )+c_2 \left (\frac {177 x^7}{280}+\frac {91 x^6}{144}+\frac {19 x^5}{30}+\frac {5 x^4}{8}+\frac {2 x^3}{3}+\frac {x^2}{2}+x\right ) \]