Internal problem ID [6407]
Book: Own collection of miscellaneous problems
Section: section 2.0
Problem number: 24.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime }-6 y^{\prime }-y x -x^{3}+2=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 31
dsolve(diff(y(x),x$2)-6*diff(y(x),x)-x*y(x)-x^3+2=0,y(x), singsol=all)
\[ y \left (x \right ) = {\mathrm e}^{3 x} \operatorname {AiryAi}\left (9+x \right ) c_{2} +{\mathrm e}^{3 x} \operatorname {AiryBi}\left (9+x \right ) c_{1} -x^{2}+12 \]
✓ Solution by Mathematica
Time used: 3.215 (sec). Leaf size: 89
DSolve[y''[x]-6*y'[x]-x*y[x]-x^3+2==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to e^{3 x} \left (\operatorname {AiryAi}(x+9) \int _1^x-e^{-3 K[1]} \pi \operatorname {AiryBi}(K[1]+9) \left (K[1]^3-2\right )dK[1]+\operatorname {AiryBi}(x+9) \int _1^xe^{-3 K[2]} \pi \operatorname {AiryAi}(K[2]+9) \left (K[2]^3-2\right )dK[2]+c_1 \operatorname {AiryAi}(x+9)+c_2 \operatorname {AiryBi}(x+9)\right ) \\ \end{align*}