Internal problem ID [5685]
Book: Differential Equations: Theory, Technique, and Practice by George Simmons, Steven Krantz.
McGraw-Hill NY. 2007. 1st Edition.
Section: Chapter 4. Power Series Solutions and Special Functions. Section 4.3. Second-Order Linear
Equations: Ordinary Points. Page 169
Problem number: 6.
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: 34
Order:=8; dsolve(diff(y(x),x$2)+x*y(x)=0,y(x),type='series',x=0);
\[ y \relax (x ) = \left (1-\frac {1}{6} x^{3}+\frac {1}{180} x^{6}\right ) y \relax (0)+\left (x -\frac {1}{12} x^{4}+\frac {1}{504} x^{7}\right ) D\relax (y )\relax (0)+O\left (x^{8}\right ) \]
✓ Solution by Mathematica
Time used: 0.001 (sec). Leaf size: 42
AsymptoticDSolveValue[y''[x]+x*y[x]==0,y[x],{x,0,7}]
\[ y(x)\to c_2 \left (\frac {x^7}{504}-\frac {x^4}{12}+x\right )+c_1 \left (\frac {x^6}{180}-\frac {x^3}{6}+1\right ) \]