56.2.32 problem 31

Internal problem ID [8836]
Book : Own collection of miscellaneous problems
Section : section 2.0
Problem number : 31
Date solved : Monday, January 27, 2025 at 05:04:06 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 16

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

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

✓ Solution by Mathematica

Time used: 0.040 (sec). Leaf size: 30

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

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