Internal problem ID [6387]
Book: Own collection of miscellaneous problems
Section: section 2.0
Problem number: 4.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {y^{\prime \prime }-x y^{\prime }-x y-x^{2}-x=0} \end {gather*}
✓ Solution by Maple
Time used: 0.008 (sec). Leaf size: 58
dsolve(diff(y(x),x$2)-x*diff(y(x),x)-x*y(x)-x^2-x=0,y(x), singsol=all)
\[ y \relax (x ) = {\mathrm e}^{-x} \left (x +2\right ) c_{2}+\left (i \sqrt {\pi }\, \sqrt {2}\, {\mathrm e}^{\frac {\left (x +2\right ) x}{2}}-\pi \left (x +2\right ) \erf \left (\frac {i \sqrt {2}\, \left (x +2\right )}{2}\right ) {\mathrm e}^{-2-x}\right ) c_{1}-x \]
✓ Solution by Mathematica
Time used: 0.755 (sec). Leaf size: 72
DSolve[y''[x]-x*y'[x]-x*y[x]-x^2-x==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{2} e^{-x} \left (-\sqrt {2 \pi } c_2 (x+2) \text {Erfi}\left (\frac {x+2}{\sqrt {2}}\right )-2 e^x x+2 \sqrt {2} c_1 (x+2)+2 c_2 e^{\frac {1}{2} (x+2)^2}\right ) \\ \end{align*}