Internal problem ID [4850]
Book: A FIRST COURSE IN DIFFERENTIAL EQUATIONS with Modeling Applications. Dennis G.
Zill. 9th edition. Brooks/Cole. CA, USA.
Section: Chapter 6. SERIES SOLUTIONS OF LINEAR EQUATIONS. Exercises. 6.3.1 page
250
Problem number: 15.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [_Lienard]
Solve \begin {gather*} \boxed {x y^{\prime \prime }-y^{\prime }+y x=0} \end {gather*} With the expansion point for the power series method at \(x = 0\).
✓ Solution by Maple
Time used: 0.078 (sec). Leaf size: 42
Order:=6; dsolve(x*diff(y(x),x$2)-diff(y(x),x)+x*y(x)=0,y(x),type='series',x=0);
\[ y \relax (x ) = c_{1} x^{2} \left (1-\frac {1}{8} x^{2}+\frac {1}{192} x^{4}+\mathrm {O}\left (x^{6}\right )\right )+c_{2} \left (\ln \relax (x ) \left (x^{2}-\frac {1}{8} x^{4}+\mathrm {O}\left (x^{6}\right )\right )+\left (-2+\frac {3}{32} x^{4}+\mathrm {O}\left (x^{6}\right )\right )\right ) \]
✓ Solution by Mathematica
Time used: 0.014 (sec). Leaf size: 59
AsymptoticDSolveValue[x*y''[x]-y'[x]+x*y[x]==0,y[x],{x,0,5}]
\[ y(x)\to c_1 \left (\frac {1}{16} \left (x^2-8\right ) x^2 \log (x)+\frac {1}{64} \left (-5 x^4+16 x^2+64\right )\right )+c_2 \left (\frac {x^6}{192}-\frac {x^4}{8}+x^2\right ) \]