Internal problem ID [6437]
Book: Own collection of miscellaneous problems
Section: section 2.0
Problem number: 50.
ODE order: 3.
ODE degree: 1.
CAS Maple gives this as type [[_3rd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {y^{\prime \prime \prime }-y^{\prime } x^{3}-y x^{2}-x^{3}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.009 (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)
\[ y \relax (x ) = -\frac {x}{2}+c_{1} \hypergeom \left (\left [\frac {1}{5}\right ], \left [\frac {3}{5}, \frac {4}{5}\right ], \frac {x^{5}}{25}\right )+c_{2} x \hypergeom \left (\left [\frac {2}{5}\right ], \left [\frac {4}{5}, \frac {6}{5}\right ], \frac {x^{5}}{25}\right )+c_{3} x^{2} \hypergeom \left (\left [\frac {3}{5}\right ], \left [\frac {6}{5}, \frac {7}{5}\right ], \frac {x^{5}}{25}\right ) \]
✓ Solution by Mathematica
Time used: 7.718 (sec). Leaf size: 2542
DSolve[y'''[x]-x^3*y'[x]-x^2*y[x]-x^3==0,y[x],x,IncludeSingularSolutions -> True]
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