Internal problem ID [9166]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 5, linear fifth and higher order
Problem number: 1587.
ODE order: 4.
ODE degree: 1.
CAS Maple gives this as type [[_high_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {x^{2} y^{\prime \prime \prime \prime }-a y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 65
dsolve(x^2*diff(y(x),x$4)-a*y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = c_{1} x \BesselJ \left (2, 2 a^{\frac {1}{4}} \sqrt {x}\right )+c_{2} x \BesselY \left (2, 2 a^{\frac {1}{4}} \sqrt {x}\right )+c_{3} x \BesselJ \left (2, 2 \sqrt {-\sqrt {a}}\, \sqrt {x}\right )+c_{4} x \BesselY \left (2, 2 \sqrt {-\sqrt {a}}\, \sqrt {x}\right ) \]
✓ Solution by Mathematica
Time used: 0.035 (sec). Leaf size: 121
DSolve[x^2*y''''[x]-a*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to c_4 G_{0,4}^{2,0}\left (\frac {a x^2}{16}| {c} 0,1,\frac {1}{2},\frac {3}{2} \\ \\ \right )+c_2 G_{0,4}^{2,0}\left (\frac {a x^2}{16}| {c} \frac {1}{2},\frac {3}{2},0,1 \\ \\ \right )+\frac {1}{64} \sqrt {a} x \left ((4 c_3-3 i c_1) J_2\left (2 \sqrt [4]{a} \sqrt {x}\right )+(3 i c_1+4 c_3) I_2\left (2 \sqrt [4]{a} \sqrt {x}\right )\right ) \\ \end{align*}