56.2.19 problem 18

Internal problem ID [8823]
Book : Own collection of miscellaneous problems
Section : section 2.0
Problem number : 18
Date solved : Monday, January 27, 2025 at 05:03:42 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime }-4 y^{\prime }-y x -x^{2}-4&=0 \end{align*}

✓ Solution by Maple

Time used: 0.014 (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)
 

\[ y = {\mathrm e}^{2 x} \operatorname {AiryAi}\left (x +4\right ) c_{2} +{\mathrm e}^{2 x} \operatorname {AiryBi}\left (x +4\right ) c_{1} -x \]

✓ Solution by Mathematica

Time used: 5.755 (sec). Leaf size: 89

DSolve[D[y[x],{x,2}]-4*D[y[x],x]-x*y[x]-x^2-4==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to e^{2 x} \left (\operatorname {AiryAi}(x+4) \int _1^x-e^{-2 K[1]} \pi \operatorname {AiryBi}(K[1]+4) \left (K[1]^2+4\right )dK[1]+\operatorname {AiryBi}(x+4) \int _1^xe^{-2 K[2]} \pi \operatorname {AiryAi}(K[2]+4) \left (K[2]^2+4\right )dK[2]+c_1 \operatorname {AiryAi}(x+4)+c_2 \operatorname {AiryBi}(x+4)\right ) \]