Internal problem ID [5884]
Book: DIFFERENTIAL EQUATIONS with Boundary Value Problems. DENNIS G. ZILL,
WARREN S. WRIGHT, MICHAEL R. CULLEN. Brooks/Cole. Boston, MA. 2013. 8th
edition.
Section: CHAPTER 6 SERIES SOLUTIONS OF LINEAR EQUATIONS. 6.4 SPECIAL
FUNCTIONS. EXERCISES 6.4. Page 267
Problem number: 22(a).
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*}
✓ Solution by Maple
Time used: 0.008 (sec). Leaf size: 29
dsolve(diff(y(x),x$2)-x^2*y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = c_{1} \sqrt {x}\, \BesselI \left (\frac {1}{4}, \frac {x^{2}}{2}\right )+c_{2} \sqrt {x}\, \BesselK \left (\frac {1}{4}, \frac {x^{2}}{2}\right ) \]
✓ Solution by Mathematica
Time used: 0.003 (sec). Leaf size: 37
DSolve[y''[x]-x^2*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to c_2 D_{-\frac {1}{2}}\left (i \sqrt {2} x\right )+c_1 D_{-\frac {1}{2}}\left (\sqrt {2} x\right ) \\ \end{align*}