Internal problem ID [1441]
Book: Elementary differential equations with boundary value problems. William F. Trench.
Brooks/Cole 2001
Section: Chapter 7 Series Solutions of Linear Second Equations. 7.6 THE METHOD OF FROBENIUS
III. Exercises 7.7. Page 389
Problem number: 25.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [_Lienard]
Solve \begin {gather*} \boxed {x y^{\prime \prime }-5 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: 32
Order:=6; dsolve(x*diff(y(x),x$2)-5*diff(y(x),x)+x*y(x)=0,y(x),type='series',x=0);
\[ y \relax (x ) = c_{1} x^{6} \left (1-\frac {1}{16} x^{2}+\frac {1}{640} x^{4}+\mathrm {O}\left (x^{6}\right )\right )+c_{2} \left (-86400-10800 x^{2}-1350 x^{4}+\mathrm {O}\left (x^{6}\right )\right ) \]
✓ Solution by Mathematica
Time used: 0.009 (sec). Leaf size: 44
AsymptoticDSolveValue[x*y''[x]-5*y'[x]+x*y[x]==0,y[x],{x,0,5}]
\[ y(x)\to c_1 \left (\frac {x^4}{64}+\frac {x^2}{8}+1\right )+c_2 \left (\frac {x^{10}}{640}-\frac {x^8}{16}+x^6\right ) \]