Internal problem ID [6401]
Book: Own collection of miscellaneous problems
Section: section 2.0
Problem number: 17.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {y^{\prime \prime }-2 y^{\prime }-y x -x^{2}-2=0} \end {gather*}
✓ Solution by Maple
Time used: 0.047 (sec). Leaf size: 24
dsolve(diff(y(x),x$2)-2*diff(y(x),x)-x*y(x)-x^2-2=0,y(x), singsol=all)
\[ y \relax (x ) = {\mathrm e}^{x} \AiryAi \left (x +1\right ) c_{2}+{\mathrm e}^{x} \AiryBi \left (x +1\right ) c_{1}-x \]
✓ Solution by Mathematica
Time used: 6.155 (sec). Leaf size: 87
DSolve[y''[x]-2*y'[x]-x*y[x]-x^2-2==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to e^x \left (\text {Ai}(x+1) \int _1^x-e^{-K[1]} \pi \text {Bi}(K[1]+1) \left (K[1]^2+2\right )dK[1]+\text {Bi}(x+1) \int _1^xe^{-K[2]} \pi \text {Ai}(K[2]+1) \left (K[2]^2+2\right )dK[2]+c_1 \text {Ai}(x+1)+c_2 \text {Bi}(x+1)\right ) \\ \end{align*}