Internal problem ID [4189]
Book: A treatise on ordinary and partial differential equations by William Woolsey Johnson.
1913
Section: Chapter VII, Solutions in series. Examples XIV. page 177
Problem number: 2.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_Emden, _Fowler]]
Solve \begin {gather*} \boxed {y^{\prime \prime }+y x=0} \end {gather*} With the expansion point for the power series method at \(x = 0\).
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 24
Order:=6; dsolve(diff(y(x),x$2)+x*y(x)=0,y(x),type='series',x=0);
\[ y \relax (x ) = \left (1-\frac {x^{3}}{6}\right ) y \relax (0)+\left (x -\frac {1}{12} x^{4}\right ) D\relax (y )\relax (0)+O\left (x^{6}\right ) \]
✓ Solution by Mathematica
Time used: 0.001 (sec). Leaf size: 28
AsymptoticDSolveValue[y''[x]+x*y[x]==0,y[x],{x,0,5}]
\[ y(x)\to c_2 \left (x-\frac {x^4}{12}\right )+c_1 \left (1-\frac {x^3}{6}\right ) \]