Internal problem ID [6387]
Book: Own collection of miscellaneous problems
Section: section 2.0
Problem number: 5.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime }-y^{\prime } x -y x -x^{3}+2=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 63
dsolve(diff(y(x),x$2)-x*diff(y(x),x)-x*y(x)-x^3+2=0,y(x), singsol=all)
\[ y \left (x \right ) = {\mathrm e}^{-x} \left (x +2\right ) c_{2} +\left (i \operatorname {erf}\left (\frac {i \sqrt {2}\, \left (x +2\right )}{2}\right ) \sqrt {\pi }\, \sqrt {2}\, \left (x +2\right ) {\mathrm e}^{-x -2}+2 \,{\mathrm e}^{\frac {x \left (x +2\right )}{2}}\right ) c_{1} -x^{2}+2 x -2 \]
✓ Solution by Mathematica
Time used: 2.335 (sec). Leaf size: 78
DSolve[y''[x]-x*y'[x]-x*y[x]-x^3+2==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) x+2)+2 \sqrt {2} c_1 (x+2)+2 c_2 e^{\frac {1}{2} (x+2)^2}\right ) \\ \end{align*}