Internal problem ID [6402]
Book: Own collection of miscellaneous problems
Section: section 2.0
Problem number: 18.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {y^{\prime \prime }-4 y^{\prime }-x y-x^{2}-4=0} \end {gather*}
✓ Solution by Maple
Time used: 0.064 (sec). Leaf size: 28
dsolve(diff(y(x),x$2)-4*diff(y(x),x)-x*y(x)-x^2-4=0,y(x), singsol=all)
\[ y \relax (x ) = {\mathrm e}^{2 x} \AiryAi \left (x +4\right ) c_{2}+{\mathrm e}^{2 x} \AiryBi \left (x +4\right ) c_{1}-x \]
✓ Solution by Mathematica
Time used: 3.815 (sec). Leaf size: 89
DSolve[y''[x]-4*y'[x]-x*y[x]-x^2-4==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to e^{2 x} \left (\text {Ai}(x+4) \int _1^x-e^{-2 K[1]} \pi \text {Bi}(K[1]+4) \left (K[1]^2+4\right )dK[1]+\text {Bi}(x+4) \int _1^xe^{-2 K[2]} \pi \text {Ai}(K[2]+4) \left (K[2]^2+4\right )dK[2]+c_1 \text {Ai}(x+4)+c_2 \text {Bi}(x+4)\right ) \\ \end{align*}