Internal problem ID [9875]
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]]
\[ \boxed {x^{2} y^{\prime \prime \prime \prime }+2 x y^{\prime \prime \prime }+a y=b \,x^{2}} \]
✓ Solution by Maple
Time used: 0.031 (sec). Leaf size: 94
dsolve(x^2*diff(y(x),x$4)+2*x*diff(y(x),x$3)+a*y(x)-b*x^2=0,y(x), singsol=all)
\[ y \left (x \right ) = \frac {c_{4} \sqrt {x}\, \operatorname {BesselY}\left (1, 2 \sqrt {-\sqrt {-a}}\, \sqrt {x}\right ) a +c_{3} \sqrt {x}\, \operatorname {BesselJ}\left (1, 2 \sqrt {-\sqrt {-a}}\, \sqrt {x}\right ) a +c_{2} \sqrt {x}\, \operatorname {BesselY}\left (1, 2 \left (-a \right )^{\frac {1}{4}} \sqrt {x}\right ) a +c_{1} \sqrt {x}\, \operatorname {BesselJ}\left (1, 2 \left (-a \right )^{\frac {1}{4}} \sqrt {x}\right ) a +b \,x^{2}}{a} \]
✗ Solution by Mathematica
Time used: 0.0 (sec). Leaf size: 0
DSolve[x^2*y''''[x]+2*x*y'''[x]+a*y[x]-b*x^2==0,y[x],x,IncludeSingularSolutions -> True]
Timed out