Internal problem ID [6403]
Book: Own collection of miscellaneous problems
Section: section 2.0
Problem number: 20.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime }-2 y^{\prime }-y x -x^{3}-x^{2}=0} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 30
dsolve(diff(y(x),x$2)-2*diff(y(x),x)-x*y(x)-x^3-x^2=0,y(x), singsol=all)
\[ y \left (x \right ) = {\mathrm e}^{x} \operatorname {AiryAi}\left (x +1\right ) c_{2} +{\mathrm e}^{x} \operatorname {AiryBi}\left (x +1\right ) c_{1} -x^{2}-x +4 \]
✓ Solution by Mathematica
Time used: 4.164 (sec). Leaf size: 91
DSolve[y''[x]-2*y'[x]-x*y[x]-x^3-x^2==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to e^x \left (\operatorname {AiryAi}(x+1) \int _1^x-e^{-K[1]} \pi \operatorname {AiryBi}(K[1]+1) K[1]^2 (K[1]+1)dK[1]+\operatorname {AiryBi}(x+1) \int _1^xe^{-K[2]} \pi \operatorname {AiryAi}(K[2]+1) K[2]^2 (K[2]+1)dK[2]+c_1 \operatorname {AiryAi}(x+1)+c_2 \operatorname {AiryBi}(x+1)\right ) \\ \end{align*}