56.2.54 problem 50

Internal problem ID [8858]
Book : Own collection of miscellaneous problems
Section : section 2.0
Problem number : 50
Date solved : Tuesday, January 28, 2025 at 03:37:04 PM
CAS classification : [[_3rd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime \prime }-x^{3} y^{\prime }-x^{2} y-x^{3}&=0 \end{align*}

✓ Solution by Maple

Time used: 0.010 (sec). Leaf size: 51

dsolve(diff(y(x),x$3)-x^3*diff(y(x),x)-x^2*y(x)-x^3=0,y(x), singsol=all)
 

\[ y = -\frac {x}{2}+c_{1} \operatorname {hypergeom}\left (\left [\frac {1}{5}\right ], \left [\frac {3}{5}, \frac {4}{5}\right ], \frac {x^{5}}{25}\right )+c_{2} x \operatorname {hypergeom}\left (\left [\frac {2}{5}\right ], \left [\frac {4}{5}, \frac {6}{5}\right ], \frac {x^{5}}{25}\right )+c_3 \,x^{2} \operatorname {hypergeom}\left (\left [\frac {3}{5}\right ], \left [\frac {6}{5}, \frac {7}{5}\right ], \frac {x^{5}}{25}\right ) \]

✓ Solution by Mathematica

Time used: 10.995 (sec). Leaf size: 2548

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

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