Internal problem ID [9131]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 4, linear fourth order
Problem number: 1552.
ODE order: 4.
ODE degree: 1.
CAS Maple gives this as type [[_high_order, _linear, _nonhomogeneous]]
Solve \begin {gather*} \boxed {x^{2} y^{\prime \prime \prime \prime }+2 x y^{\prime \prime \prime }+a y-b \,x^{2}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 89
dsolve(x^2*diff(diff(diff(diff(y(x),x),x),x),x)+2*x*diff(diff(diff(y(x),x),x),x)+a*y(x)-b*x^2=0,y(x), singsol=all)
\[ y \relax (x ) = \frac {b \,x^{2}}{a}+c_{1} \sqrt {x}\, \BesselJ \left (1, 2 \left (-a \right )^{\frac {1}{4}} \sqrt {x}\right )+c_{2} \sqrt {x}\, \BesselY \left (1, 2 \left (-a \right )^{\frac {1}{4}} \sqrt {x}\right )+c_{3} \sqrt {x}\, \BesselJ \left (1, 2 \sqrt {-\sqrt {-a}}\, \sqrt {x}\right )+c_{4} \sqrt {x}\, \BesselY \left (1, 2 \sqrt {-\sqrt {-a}}\, \sqrt {x}\right ) \]
✗ Solution by Mathematica
Time used: 0.0 (sec). Leaf size: 0
DSolve[-(b*x^2) + a*y[x] + 2*x*Derivative[3][y][x] + x^2*Derivative[4][y][x] == 0,y[x],x,IncludeSingularSolutions -> True]
Timed out