Internal problem ID [6408]
Book: Own collection of miscellaneous problems
Section: section 2.0
Problem number: 25.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime }-8 y^{\prime }-y x -x^{3}+2=0} \]
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 31
dsolve(diff(y(x),x$2)-8*diff(y(x),x)-x*y(x)-x^3+2=0,y(x), singsol=all)
\[ y \left (x \right ) = {\mathrm e}^{4 x} \operatorname {AiryAi}\left (16+x \right ) c_{2} +{\mathrm e}^{4 x} \operatorname {AiryBi}\left (16+x \right ) c_{1} -x^{2}+16 \]
✓ Solution by Mathematica
Time used: 3.178 (sec). Leaf size: 89
DSolve[y''[x]-8*y'[x]-x*y[x]-x^3+2==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to e^{4 x} \left (\operatorname {AiryAi}(x+16) \int _1^x-e^{-4 K[1]} \pi \operatorname {AiryBi}(K[1]+16) \left (K[1]^3-2\right )dK[1]+\operatorname {AiryBi}(x+16) \int _1^xe^{-4 K[2]} \pi \operatorname {AiryAi}(K[2]+16) \left (K[2]^3-2\right )dK[2]+c_1 \operatorname {AiryAi}(x+16)+c_2 \operatorname {AiryBi}(x+16)\right ) \\ \end{align*}