67.2.1 problem Problem 1(a)

Internal problem ID [13958]
Book : APPLIED DIFFERENTIAL EQUATIONS The Primary Course by Vladimir A. Dobrushkin. CRC Press 2015
Section : Chapter 4, Second and Higher Order Linear Differential Equations. Problems page 221
Problem number : Problem 1(a)
Date solved : Tuesday, January 28, 2025 at 06:09:43 AM
CAS classification : [[_Emden, _Fowler]]

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

✓ Solution by Maple

Time used: 0.030 (sec). Leaf size: 27

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

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

✓ Solution by Mathematica

Time used: 0.022 (sec). Leaf size: 30

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

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