Internal problem ID [6389]
Book: Own collection of miscellaneous problems
Section: section 2.0
Problem number: 6.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
Solve \begin {gather*} \boxed {y^{\prime \prime }-x y^{\prime }-y x -x^{4}-6=0} \end {gather*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 67
dsolve(diff(y(x),x$2)-x*diff(y(x),x)-x*y(x)-x^4-6=0,y(x), singsol=all)
\[ y \relax (x ) = {\mathrm e}^{-x} \left (x +2\right ) c_{2}+\left (\left (x +2\right ) \pi \erf \left (\frac {i \sqrt {2}\, \left (x +2\right )}{2}\right ) {\mathrm e}^{-x -2}-i \sqrt {\pi }\, \sqrt {2}\, {\mathrm e}^{\frac {x \left (x +2\right )}{2}}\right ) c_{1}-x^{3}+3 x^{2}-6 x \]
✓ Solution by Mathematica
Time used: 3.52 (sec). Leaf size: 79
DSolve[y''[x]-x*y'[x]-x*y[x]-x^4-6==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 ((x-3) x+6)+2 \sqrt {2} c_1 (x+2)+2 c_2 e^{\frac {1}{2} (x+2)^2}\right ) \\ \end{align*}