Internal problem ID [6408]
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]]
Solve \begin {gather*} \boxed {y^{\prime \prime }-6 y^{\prime }-x y-x^{3}+2=0} \end {gather*}
✓ Solution by Maple
Time used: 0.066 (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)
\[ y \relax (x ) = {\mathrm e}^{3 x} \AiryAi \left (9+x \right ) c_{2}+{\mathrm e}^{3 x} \AiryBi \left (9+x \right ) c_{1}-x^{2}+12 \]
✓ Solution by Mathematica
Time used: 3.975 (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 (\text {Ai}(x+9) \int _1^x-e^{-3 K[1]} \pi \text {Bi}(K[1]+9) \left (K[1]^3-2\right )dK[1]+\text {Bi}(x+9) \int _1^xe^{-3 K[2]} \pi \text {Ai}(K[2]+9) \left (K[2]^3-2\right )dK[2]+c_1 \text {Ai}(x+9)+c_2 \text {Bi}(x+9)\right ) \\ \end{align*}