Internal problem ID [10874]
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).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_Emden, _Fowler]]
\[ \boxed {y^{\prime \prime }+x^{2} y=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 29
dsolve(diff(y(x),x$2)+x^2*y(x)=0,y(x), singsol=all)
\[ y \left (x \right ) = c_{1} \sqrt {x}\, \operatorname {BesselJ}\left (\frac {1}{4}, \frac {x^{2}}{2}\right )+c_{2} \sqrt {x}\, \operatorname {BesselY}\left (\frac {1}{4}, \frac {x^{2}}{2}\right ) \]
✓ Solution by Mathematica
Time used: 0.004 (sec). Leaf size: 30
DSolve[y''[x]+x^2*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} 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 ) \\ \end{align*}