Internal problem ID [6637]
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]]
\[ \boxed {y^{\prime \prime }-y x^{2}=0} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 27
dsolve(diff(y(x),x$2)-x^2*y(x)=0,y(x), singsol=all)
\[ y \left (x \right ) = \left (\operatorname {BesselK}\left (\frac {1}{4}, \frac {x^{2}}{2}\right ) c_{2} +\operatorname {BesselI}\left (\frac {1}{4}, \frac {x^{2}}{2}\right ) c_{1} \right ) \sqrt {x} \]
✓ Solution by Mathematica
Time used: 0.021 (sec). Leaf size: 37
DSolve[y''[x]-x^2*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to c_2 \operatorname {ParabolicCylinderD}\left (-\frac {1}{2},i \sqrt {2} x\right )+c_1 \operatorname {ParabolicCylinderD}\left (-\frac {1}{2},\sqrt {2} x\right ) \]