Internal problem ID [8666]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 2, linear second order
Problem number: 1086.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_Emden, _Fowler]]
Solve \begin {gather*} \boxed {4 y^{\prime \prime }+9 y x=0} \end {gather*}
✓ Solution by Maple
Time used: 0.003 (sec). Leaf size: 29
dsolve(4*diff(diff(y(x),x),x)+9*x*y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = c_{1} \AiryAi \left (-\frac {3^{\frac {2}{3}} 2^{\frac {1}{3}} x}{2}\right )+c_{2} \AiryBi \left (-\frac {3^{\frac {2}{3}} 2^{\frac {1}{3}} x}{2}\right ) \]
✓ Solution by Mathematica
Time used: 0.003 (sec). Leaf size: 42
DSolve[9*x*y[x] + 4*y''[x] == 0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to c_1 \text {Ai}\left (x \text {Root}\left [4 \text {$\#$1}^3+9\&,3\right ]\right )+c_2 \text {Bi}\left (x \text {Root}\left [4 \text {$\#$1}^3+9\&,3\right ]\right ) \\ \end{align*}