Internal problem ID [6148]
Book: Elementary differential equations. Rainville, Bedient, Bedient. Prentice Hall. NJ. 8th edition.
1997.
Section: CHAPTER 17. Power series solutions. 17.5. Solutions Near an Ordinary Point. Exercises page
355
Problem number: 13.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_Emden, _Fowler]]
Solve \begin {gather*} \boxed {y^{\prime \prime }+y x^{2}=0} \end {gather*} With the expansion point for the power series method at \(x = 0\).
✓ Solution by Maple
Time used: 0.001 (sec). Leaf size: 24
Order:=8; dsolve(diff(y(x),x$2)+x^2*y(x)=0,y(x),type='series',x=0);
\[ y \relax (x ) = \left (1-\frac {x^{4}}{12}\right ) y \relax (0)+\left (x -\frac {1}{20} x^{5}\right ) D\relax (y )\relax (0)+O\left (x^{8}\right ) \]
✓ Solution by Mathematica
Time used: 0.001 (sec). Leaf size: 28
AsymptoticDSolveValue[y''[x]+x^2*y[x]==0,y[x],{x,0,7}]
\[ y(x)\to c_2 \left (x-\frac {x^5}{20}\right )+c_1 \left (1-\frac {x^4}{12}\right ) \]