Internal problem ID [2446]
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 11.5. page
771
Problem number: 13.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_Emden, _Fowler]]
Solve \begin {gather*} \boxed {x y^{\prime \prime }-y=0} \end {gather*} With the expansion point for the power series method at \(x = 0\).
✓ Solution by Maple
Time used: 0.013 (sec). Leaf size: 58
Order:=6; dsolve(x*diff(y(x),x$2)-y(x)=0,y(x),type='series',x=0);
\[ y \relax (x ) = c_{1} x \left (1+\frac {1}{2} x +\frac {1}{12} x^{2}+\frac {1}{144} x^{3}+\frac {1}{2880} x^{4}+\frac {1}{86400} x^{5}+\mathrm {O}\left (x^{6}\right )\right )+c_{2} \left (\ln \relax (x ) \left (x +\frac {1}{2} x^{2}+\frac {1}{12} x^{3}+\frac {1}{144} x^{4}+\frac {1}{2880} x^{5}+\mathrm {O}\left (x^{6}\right )\right )+\left (1-\frac {3}{4} x^{2}-\frac {7}{36} x^{3}-\frac {35}{1728} x^{4}-\frac {101}{86400} x^{5}+\mathrm {O}\left (x^{6}\right )\right )\right ) \]
✓ Solution by Mathematica
Time used: 0.016 (sec). Leaf size: 85
AsymptoticDSolveValue[x*y''[x]-y[x]==0,y[x],{x,0,5}]
\[ y(x)\to c_1 \left (\frac {1}{144} x \left (x^3+12 x^2+72 x+144\right ) \log (x)+\frac {-47 x^4-480 x^3-2160 x^2-1728 x+1728}{1728}\right )+c_2 \left (\frac {x^5}{2880}+\frac {x^4}{144}+\frac {x^3}{12}+\frac {x^2}{2}+x\right ) \]