Internal problem ID [7178]
Book: Own collection of miscellaneous problems
Section: section 2.0
Problem number: 41.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {y^{\prime \prime }-x^{2} y^{\prime }-x^{2} y=x^{2}} \]
✓ Solution by Maple
Time used: 0.031 (sec). Leaf size: 55
dsolve(diff(y(x),x$2)-x^2*diff(y(x),x)-x^2*y(x)-x^2=0,y(x), singsol=all)
\[ y \left (x \right ) = \operatorname {HeunT}\left (3^{\frac {2}{3}}, 3, 2 \,3^{\frac {1}{3}}, \frac {3^{\frac {2}{3}} x}{3}\right ) {\mathrm e}^{-x} c_{2} +\operatorname {HeunT}\left (3^{\frac {2}{3}}, -3, 2 \,3^{\frac {1}{3}}, -\frac {3^{\frac {2}{3}} x}{3}\right ) {\mathrm e}^{\frac {x \left (x^{2}+3\right )}{3}} c_{1} -1 \]
✗ Solution by Mathematica
Time used: 0.0 (sec). Leaf size: 0
DSolve[y''[x]-x^2*y'[x]-x^2*y[x]-x^2==0,y[x],x,IncludeSingularSolutions -> True]
Not solved