Internal problem ID [2450]
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: 17.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_Emden, _Fowler]]
Solve \begin {gather*} \boxed {x y^{\prime \prime }+y^{\prime }-2 y=0} \end {gather*} With the expansion point for the power series method at \(x = 0\).
✓ Solution by Maple
Time used: 0.012 (sec). Leaf size: 59
Order:=6; dsolve(x*diff(y(x),x$2)+diff(y(x),x)-2*y(x)=0,y(x),type='series',x=0);
\[ y \relax (x ) = \left (\ln \relax (x ) c_{2}+c_{1}\right ) \left (1+2 x +x^{2}+\frac {2}{9} x^{3}+\frac {1}{36} x^{4}+\frac {1}{450} x^{5}+\mathrm {O}\left (x^{6}\right )\right )+\left (\left (-4\right ) x -3 x^{2}-\frac {22}{27} x^{3}-\frac {25}{216} x^{4}-\frac {137}{13500} x^{5}+\mathrm {O}\left (x^{6}\right )\right ) c_{2} \]
✓ Solution by Mathematica
Time used: 0.003 (sec). Leaf size: 101
AsymptoticDSolveValue[x*y''[x]+y'[x]-2*y[x]==0,y[x],{x,0,5}]
\[ y(x)\to c_1 \left (\frac {x^5}{450}+\frac {x^4}{36}+\frac {2 x^3}{9}+x^2+2 x+1\right )+c_2 \left (-\frac {137 x^5}{13500}-\frac {25 x^4}{216}-\frac {22 x^3}{27}-3 x^2+\left (\frac {x^5}{450}+\frac {x^4}{36}+\frac {2 x^3}{9}+x^2+2 x+1\right ) \log (x)-4 x\right ) \]