Internal problem ID [6402]
Book: Own collection of miscellaneous problems
Section: section 2.0
Problem number: 19.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime }-y^{\prime }-y x -x^{3}+1=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 75
dsolve(diff(y(x),x$2)-diff(y(x),x)-x*y(x)-x^3+1=0,y(x), singsol=all)
\[ y \left (x \right ) = {\mathrm e}^{\frac {x}{2}} \operatorname {AiryAi}\left (\frac {1}{4}+x \right ) c_{2} +{\mathrm e}^{\frac {x}{2}} \operatorname {AiryBi}\left (\frac {1}{4}+x \right ) c_{1} +\pi \,{\mathrm e}^{\frac {x}{2}} \left (-\left (\int \left (x^{3}-1\right ) \operatorname {AiryBi}\left (\frac {1}{4}+x \right ) {\mathrm e}^{-\frac {x}{2}}d x \right ) \operatorname {AiryAi}\left (\frac {1}{4}+x \right )+\left (\int \left (x^{3}-1\right ) \operatorname {AiryAi}\left (\frac {1}{4}+x \right ) {\mathrm e}^{-\frac {x}{2}}d x \right ) \operatorname {AiryBi}\left (\frac {1}{4}+x \right )\right ) \]
✓ Solution by Mathematica
Time used: 1.781 (sec). Leaf size: 107
DSolve[y''[x]-y'[x]-x*y[x]-x^3+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]^3-1\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]^3-1\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*}