56.2.23 problem 22

Internal problem ID [8827]
Book : Own collection of miscellaneous problems
Section : section 2.0
Problem number : 22
Date solved : Monday, January 27, 2025 at 05:03:46 PM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }-2 y^{\prime }-y x -x^{3}+2&=0 \end{align*}

✓ Solution by Maple

Time used: 0.014 (sec). Leaf size: 27

dsolve(diff(y(x),x$2)-2*diff(y(x),x)-x*y(x)-x^3+2=0,y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 2.525 (sec). Leaf size: 87

DSolve[D[y[x],{x,2}]-2*D[y[x],x]-x*y[x]-x^3+2==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to e^x \left (\operatorname {AiryAi}(x+1) \int _1^x-e^{-K[1]} \pi \operatorname {AiryBi}(K[1]+1) \left (K[1]^3-2\right )dK[1]+\operatorname {AiryBi}(x+1) \int _1^xe^{-K[2]} \pi \operatorname {AiryAi}(K[2]+1) \left (K[2]^3-2\right )dK[2]+c_1 \operatorname {AiryAi}(x+1)+c_2 \operatorname {AiryBi}(x+1)\right ) \]