56.2.46 problem 45

Internal problem ID [8850]
Book : Own collection of miscellaneous problems
Section : section 2.0
Problem number : 45
Date solved : Tuesday, January 28, 2025 at 03:24:10 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

✓ Solution by Maple

Time used: 0.179 (sec). Leaf size: 57

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

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

✗ Solution by Mathematica

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

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

Not solved