56.2.31 problem 30

Internal problem ID [8835]
Book : Own collection of miscellaneous problems
Section : section 2.0
Problem number : 30
Date solved : Monday, January 27, 2025 at 05:04:04 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 14

dsolve(diff(y(x),x$2)-x*y(x)-x=0,y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.040 (sec). Leaf size: 28

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

\[ y(x)\to \pi \operatorname {AiryAiPrime}(x) \operatorname {AiryBi}(x)+c_2 \operatorname {AiryBi}(x)+\operatorname {AiryAi}(x) (-\pi \operatorname {AiryBiPrime}(x)+c_1) \]