Internal problem ID [7183]
Book: Own collection of miscellaneous problems
Section: section 2.0
Problem number: 46.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {y^{\prime \prime }-x^{2} y^{\prime }-y x^{3}=x^{4}+x^{2}} \]
✓ Solution by Maple
Time used: 0.031 (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)
\[ y \left (x \right ) = {\mathrm e}^{-\frac {x \left (x -2\right )}{2}} \operatorname {HeunT}\left (2 \,3^{\frac {2}{3}}, -3, -3 \,3^{\frac {1}{3}}, \frac {3^{\frac {2}{3}} \left (x +1\right )}{3}\right ) c_{2} +{\mathrm e}^{\frac {1}{3} x^{3}+\frac {1}{2} x^{2}-x} \operatorname {HeunT}\left (2 \,3^{\frac {2}{3}}, 3, -3 \,3^{\frac {1}{3}}, -\frac {3^{\frac {2}{3}} \left (x +1\right )}{3}\right ) c_{1} -x \]
✗ Solution by Mathematica
Time used: 0.0 (sec). Leaf size: 0
DSolve[y''[x]-x^2*y'[x]-x^3*y[x]-x^4-x^2==0,y[x],x,IncludeSingularSolutions -> True]
Not solved