Internal problem ID [9432]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 2, linear second order
Problem number: 1102.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_Emden, _Fowler]]
\[ \boxed {y^{\prime \prime } x +2 y^{\prime }+a \,x^{2} y=0} \]
✓ Solution by Maple
Time used: 0.047 (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)
\[ y \left (x \right ) = \frac {c_{1} \operatorname {BesselJ}\left (\frac {1}{3}, \frac {2 \sqrt {a}\, x^{\frac {3}{2}}}{3}\right )+c_{2} \operatorname {BesselY}\left (\frac {1}{3}, \frac {2 \sqrt {a}\, x^{\frac {3}{2}}}{3}\right )}{\sqrt {x}} \]
✓ Solution by Mathematica
Time used: 0.021 (sec). Leaf size: 36
DSolve[a*x^2*y[x] + 2*y'[x] + x*y''[x] == 0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {c_1 \operatorname {AiryAi}\left (\sqrt [3]{-a} x\right )+c_2 \operatorname {AiryBi}\left (\sqrt [3]{-a} x\right )}{x} \]