Internal problem ID [2403]
Book: Differential equations and linear algebra, Stephen W. Goode and Scott A Annin. Fourth edition,
2015
Section: Chapter 11, Series Solutions to Linear Differential Equations. Exercises for 11.2. page
739
Problem number: Problem 17.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {x y^{\prime \prime }-\left (x -1\right ) y^{\prime }-y x=0} \end {gather*} With the expansion point for the power series method at \(x = 0\).
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 53
Order:=6; dsolve(x*diff(y(x),x$2)-(x-1)*diff(y(x),x)-x*y(x)=0,y(x),type='series',x=0);
\[ y \relax (x ) = \left (c_{2} \ln \relax (x )+c_{1}\right ) \left (1+\frac {1}{4} x^{2}+\frac {1}{18} x^{3}+\frac {5}{192} x^{4}+\frac {23}{3600} x^{5}+\mathrm {O}\left (x^{6}\right )\right )+\left (x +\frac {11}{108} x^{3}+\frac {11}{1152} x^{4}+\frac {883}{216000} x^{5}+\mathrm {O}\left (x^{6}\right )\right ) c_{2} \]
✓ Solution by Mathematica
Time used: 0.005 (sec). Leaf size: 96
AsymptoticDSolveValue[x*y''[x]-(x-1)*y'[x]-x*y[x]==0,y[x],{x,0,5}]
\[ y(x)\to c_1 \left (\frac {23 x^5}{3600}+\frac {5 x^4}{192}+\frac {x^3}{18}+\frac {x^2}{4}+1\right )+c_2 \left (\frac {883 x^5}{216000}+\frac {11 x^4}{1152}+\frac {11 x^3}{108}+\left (\frac {23 x^5}{3600}+\frac {5 x^4}{192}+\frac {x^3}{18}+\frac {x^2}{4}+1\right ) \log (x)+x\right ) \]