Internal problem ID [10830]
Book: Differential equations and the calculus of variations by L. ElSGOLTS. MIR PUBLISHERS,
MOSCOW, Third printing 1977.
Section: Chapter 2, DIFFERENTIAL EQUATIONS OF THE SECOND ORDER AND HIGHER.
Problems page 172
Problem number: Problem 15.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_Emden, _Fowler]]
\[ \boxed {y^{\prime \prime }+4 x y=0} \] With the expansion point for the power series method at \(x = 0\).
✓ Solution by Maple
Time used: 0.219 (sec). Leaf size: 24
Order:=6; dsolve(diff(y(x),x$2)+4*x*y(x)=0,y(x),type='series',x=0);
\[ y \left (x \right ) = \left (1-\frac {2 x^{3}}{3}\right ) y \left (0\right )+\left (x -\frac {1}{3} x^{4}\right ) D\left (y \right )\left (0\right )+O\left (x^{6}\right ) \]
✓ Solution by Mathematica
Time used: 0.001 (sec). Leaf size: 28
AsymptoticDSolveValue[y''[x]+4*x*y[x]==0,y[x],{x,0,5}]
\[ y(x)\to c_2 \left (x-\frac {x^4}{3}\right )+c_1 \left (1-\frac {2 x^3}{3}\right ) \]