Internal problem ID [7170]
Book: Own collection of miscellaneous problems
Section: section 2.0
Problem number: 33.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime }-y x=x^{6}+x^{3}-42} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 23
dsolve(diff(y(x),x$2)-x*y(x)-x^6-x^3+42=0,y(x), singsol=all)
\[ y \left (x \right ) = \operatorname {AiryAi}\left (x \right ) c_{2} +\operatorname {AiryBi}\left (x \right ) c_{1} -x^{5}-21 x^{2} \]
✓ Solution by Mathematica
Time used: 1.142 (sec). Leaf size: 367
DSolve[y''[x]-x*y[x]-x^6-x^3+42==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to -\frac {-126 \sqrt [3]{3} \pi x \operatorname {Gamma}\left (\frac {1}{3}\right ) \left (\sqrt {3} \operatorname {AiryAi}(x)-\operatorname {AiryBi}(x)\right ) \, _1F_2\left (\frac {1}{3};\frac {2}{3},\frac {4}{3};\frac {x^3}{9}\right )+\frac {\sqrt [6]{3} \pi x^8 \operatorname {Gamma}\left (\frac {2}{3}\right ) \operatorname {Gamma}\left (\frac {8}{3}\right ) \left (3 \operatorname {AiryAi}(x)+\sqrt {3} \operatorname {AiryBi}(x)\right ) \, _1F_2\left (\frac {8}{3};\frac {4}{3},\frac {11}{3};\frac {x^3}{9}\right )}{\operatorname {Gamma}\left (\frac {11}{3}\right )}+\frac {3 \sqrt [3]{3} \pi x^7 \operatorname {Gamma}\left (\frac {4}{3}\right ) \operatorname {Gamma}\left (\frac {7}{3}\right ) \left (\sqrt {3} \operatorname {AiryAi}(x)-\operatorname {AiryBi}(x)\right ) \, _1F_2\left (\frac {7}{3};\frac {2}{3},\frac {10}{3};\frac {x^3}{9}\right )}{\operatorname {Gamma}\left (\frac {10}{3}\right )}+\frac {\sqrt [6]{3} \pi x^5 \operatorname {Gamma}\left (\frac {2}{3}\right ) \operatorname {Gamma}\left (\frac {5}{3}\right ) \left (3 \operatorname {AiryAi}(x)+\sqrt {3} \operatorname {AiryBi}(x)\right ) \, _1F_2\left (\frac {5}{3};\frac {4}{3},\frac {8}{3};\frac {x^3}{9}\right )}{\operatorname {Gamma}\left (\frac {8}{3}\right )}+\frac {3 \sqrt [3]{3} \pi x^4 \operatorname {Gamma}\left (\frac {4}{3}\right )^2 \left (\sqrt {3} \operatorname {AiryAi}(x)-\operatorname {AiryBi}(x)\right ) \, _1F_2\left (\frac {4}{3};\frac {2}{3},\frac {7}{3};\frac {x^3}{9}\right )}{\operatorname {Gamma}\left (\frac {7}{3}\right )}-\frac {42 \sqrt [6]{3} \pi x^2 \operatorname {Gamma}\left (\frac {2}{3}\right )^2 \left (3 \operatorname {AiryAi}(x)+\sqrt {3} \operatorname {AiryBi}(x)\right ) \, _1F_2\left (\frac {2}{3};\frac {4}{3},\frac {5}{3};\frac {x^3}{9}\right )}{\operatorname {Gamma}\left (\frac {5}{3}\right )}-27 \operatorname {Gamma}\left (\frac {2}{3}\right ) \operatorname {Gamma}\left (\frac {4}{3}\right ) (c_1 \operatorname {AiryAi}(x)+c_2 \operatorname {AiryBi}(x))}{27 \operatorname {Gamma}\left (\frac {2}{3}\right ) \operatorname {Gamma}\left (\frac {4}{3}\right )} \]