60.5.17 problem 1552

Internal problem ID [11551]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 4, linear fourth order
Problem number : 1552
Date solved : Tuesday, January 28, 2025 at 06:06:49 PM
CAS classification : [[_high_order, _linear, _nonhomogeneous]]

\begin{align*} x^{2} y^{\prime \prime \prime \prime }+2 x y^{\prime \prime \prime }+a y-b \,x^{2}&=0 \end{align*}

✓ Solution by Maple

Time used: 0.039 (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)
 

\[ y = \frac {c_4 \sqrt {x}\, \operatorname {BesselY}\left (1, 2 \sqrt {-\sqrt {-a}}\, \sqrt {x}\right ) a +c_{1} \sqrt {x}\, \operatorname {BesselJ}\left (1, 2 \left (-a \right )^{{1}/{4}} \sqrt {x}\right ) a +c_{2} \sqrt {x}\, \operatorname {BesselY}\left (1, 2 \left (-a \right )^{{1}/{4}} \sqrt {x}\right ) a +c_3 \sqrt {x}\, \operatorname {BesselJ}\left (1, 2 \sqrt {-\sqrt {-a}}\, \sqrt {x}\right ) a +b \,x^{2}}{a} \]

✗ Solution by Mathematica

Time used: 0.000 (sec). Leaf size: 0

DSolve[x^2*D[y[x],{x,4}]+2*x*D[y[x],{x,3}]+a*y[x]-b*x^2==0,y[x],x,IncludeSingularSolutions -> True]
 

Timed out