56.2.47 problem 46

Internal problem ID [8851]
Book : Own collection of miscellaneous problems
Section : section 2.0
Problem number : 46
Date solved : Tuesday, January 28, 2025 at 03:24:11 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime }-x^{2} y^{\prime }-x^{3} y-x^{4}-x^{2}&=0 \end{align*}

✓ Solution by Maple

Time used: 0.216 (sec). Leaf size: 74

dsolve(diff(y(x),x$2)-x^2*diff(y(x),x)-x^3*y(x)-x^4-x^2=0,y(x), singsol=all)
 

\[ y = {\mathrm e}^{-\frac {x \left (x -2\right )}{2}} \operatorname {HeunT}\left (2 \,3^{{2}/{3}}, -3, -3 \,3^{{1}/{3}}, \frac {3^{{2}/{3}} \left (x +1\right )}{3}\right ) c_{2} +{\mathrm e}^{\frac {1}{3} x^{3}+\frac {1}{2} x^{2}-x} \operatorname {HeunT}\left (2 \,3^{{2}/{3}}, 3, -3 \,3^{{1}/{3}}, -\frac {3^{{2}/{3}} \left (x +1\right )}{3}\right ) c_{1} -x \]

✗ Solution by Mathematica

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

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

Not solved