52.3.19 problem 22(a)

Internal problem ID [8305]
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)
Date solved : Monday, January 27, 2025 at 03:48:26 PM
CAS classification : [[_Emden, _Fowler]]

\begin{align*} y^{\prime \prime }-x^{2} y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.009 (sec). Leaf size: 27

dsolve(diff(y(x),x$2)-x^2*y(x)=0,y(x), singsol=all)
 

\[ y = \left (\operatorname {BesselK}\left (\frac {1}{4}, \frac {x^{2}}{2}\right ) c_{2} +\operatorname {BesselI}\left (\frac {1}{4}, \frac {x^{2}}{2}\right ) c_{1} \right ) \sqrt {x} \]

✓ Solution by Mathematica

Time used: 0.020 (sec). Leaf size: 37

DSolve[D[y[x],{x,2}]-x^2*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to c_2 \operatorname {ParabolicCylinderD}\left (-\frac {1}{2},i \sqrt {2} x\right )+c_1 \operatorname {ParabolicCylinderD}\left (-\frac {1}{2},\sqrt {2} x\right ) \]