Internal problem ID [6398]
Book: Own collection of miscellaneous problems
Section: section 2.0
Problem number: 16.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {y^{\prime \prime }-y^{\prime }-y x -x^{2}-1=0} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 28
dsolve(diff(y(x),x$2)-diff(y(x),x)-x*y(x)-x^2-1=0,y(x), singsol=all)
\[ y \left (x \right ) = {\mathrm e}^{\frac {x}{2}} \operatorname {AiryAi}\left (\frac {1}{4}+x \right ) c_{2} +{\mathrm e}^{\frac {x}{2}} \operatorname {AiryBi}\left (\frac {1}{4}+x \right ) c_{1} -x \]
✓ Solution by Mathematica
Time used: 2.036 (sec). Leaf size: 107
DSolve[y''[x]-y'[x]-x*y[x]-x^2-1==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to e^{x/2} \left (\operatorname {AiryAi}\left (x+\frac {1}{4}\right ) \int _1^x-e^{-\frac {K[1]}{2}} \pi \operatorname {AiryBi}\left (K[1]+\frac {1}{4}\right ) \left (K[1]^2+1\right )dK[1]+\operatorname {AiryBi}\left (x+\frac {1}{4}\right ) \int _1^xe^{-\frac {K[2]}{2}} \pi \operatorname {AiryAi}\left (K[2]+\frac {1}{4}\right ) \left (K[2]^2+1\right )dK[2]+c_1 \operatorname {AiryAi}\left (x+\frac {1}{4}\right )+c_2 \operatorname {AiryBi}\left (x+\frac {1}{4}\right )\right ) \\ \end{align*}