60.3.98 problem 1102

Internal problem ID [11108]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 2, linear second order
Problem number : 1102
Date solved : Monday, January 27, 2025 at 10:45:58 PM
CAS classification : [[_Emden, _Fowler]]

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

✓ Solution by Maple

Time used: 0.082 (sec). Leaf size: 33

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

\[ y = \frac {c_{2} \operatorname {BesselY}\left (\frac {1}{3}, \frac {2 \sqrt {a}\, x^{{3}/{2}}}{3}\right )+c_{1} \operatorname {BesselJ}\left (\frac {1}{3}, \frac {2 \sqrt {a}\, x^{{3}/{2}}}{3}\right )}{\sqrt {x}} \]

✓ Solution by Mathematica

Time used: 0.022 (sec). Leaf size: 36

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

\[ y(x)\to \frac {c_1 \operatorname {AiryAi}\left (\sqrt [3]{-a} x\right )+c_2 \operatorname {AiryBi}\left (\sqrt [3]{-a} x\right )}{x} \]