Internal problem ID [6485]
Book: Own collection of miscellaneous problems
Section: section 4.0
Problem number: 17.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [_Lienard]
Solve \begin {gather*} \boxed {x y^{\prime \prime }+2 y^{\prime }+x y=0} \end {gather*} With initial conditions \begin {align*} [y \relax (0) = 1, y^{\prime }\relax (0) = 0] \end {align*}
With the expansion point for the power series method at \(x = 0\).
✓ Solution by Maple
Time used: 0.047 (sec). Leaf size: 14
Order:=6; dsolve([x*diff(y(x),x$2)+2*diff(y(x),x)+x*y(x)=0,y(0) = 1, D(y)(0) = 0],y(x),type='series',x=0);
\[ y \relax (x ) = 1-\frac {1}{6} x^{2}+\frac {1}{120} x^{4}+\mathrm {O}\left (x^{6}\right ) \]
✓ Solution by Mathematica
Time used: 0.008 (sec). Leaf size: 19
AsymptoticDSolveValue[{x*y''[x]+2*y'[x]+x*y[x]==0,{y[0]==1,y'[0]==0}},y[x],{x,0,5}]
\[ y(x)\to \frac {x^4}{120}-\frac {x^2}{6}+1 \]