Internal problem ID [7142]
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]]
\[ \boxed {y^{\prime \prime }-x y^{\prime }-y x=x^{4}+6} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 66
dsolve(diff(y(x),x$2)-x*diff(y(x),x)-x*y(x)-x^4-6=0,y(x), singsol=all)
\[ y \left (x \right ) = \pi \,{\mathrm e}^{-2-x} c_{1} \left (x +2\right ) \operatorname {erf}\left (\frac {i \sqrt {2}\, \left (x +2\right )}{2}\right )-i \sqrt {\pi }\, \sqrt {2}\, {\mathrm e}^{\frac {x \left (x +2\right )}{2}} c_{1} +{\mathrm e}^{-x} \left (x +2\right ) c_{2} -x^{3}+3 x^{2}-6 x \]
✓ Solution by Mathematica
Time used: 7.359 (sec). Leaf size: 92
DSolve[y''[x]-x*y'[x]-x*y[x]-x^4-6==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {1}{2} e^{-x} \left (-\sqrt {2 \pi } c_2 \sqrt {(x+2)^2} \text {erfi}\left (\frac {\sqrt {(x+2)^2}}{\sqrt {2}}\right )-2 e^x x \left (x^2-3 x+6\right )+2 \sqrt {2} c_1 (x+2)+2 c_2 e^{\frac {1}{2} (x+2)^2}\right ) \]