Internal problem ID [6412]
Book: Own collection of miscellaneous problems
Section: section 2.0
Problem number: 29.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime }-y x -x^{6}+64=0} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 143
dsolve(diff(y(x),x$2)-x*y(x)-x^6+64=0,y(x), singsol=all)
\[ y \left (x \right ) = \operatorname {AiryAi}\left (x \right ) c_{2} +\operatorname {AiryBi}\left (x \right ) c_{1} -\frac {\left (-\frac {16 x^{6} \pi \left (\operatorname {AiryBi}\left (x \right ) 3^{\frac {1}{3}}-3^{\frac {5}{6}} \operatorname {AiryAi}\left (x \right )\right ) \operatorname {hypergeom}\left (\left [\frac {7}{3}\right ], \left [\frac {2}{3}, \frac {10}{3}\right ], \frac {x^{3}}{9}\right )}{21}+x^{7} \Gamma \left (\frac {2}{3}\right )^{2} \left (3^{\frac {1}{6}} \operatorname {AiryBi}\left (x \right )+3^{\frac {2}{3}} \operatorname {AiryAi}\left (x \right )\right ) \operatorname {hypergeom}\left (\left [\frac {8}{3}\right ], \left [\frac {4}{3}, \frac {11}{3}\right ], \frac {x^{3}}{9}\right )+\frac {1024 \pi \left (\operatorname {AiryBi}\left (x \right ) 3^{\frac {1}{3}}-3^{\frac {5}{6}} \operatorname {AiryAi}\left (x \right )\right ) \operatorname {hypergeom}\left (\left [\frac {1}{3}\right ], \left [\frac {2}{3}, \frac {4}{3}\right ], \frac {x^{3}}{9}\right )}{3}-256 x \operatorname {hypergeom}\left (\left [\frac {2}{3}\right ], \left [\frac {4}{3}, \frac {5}{3}\right ], \frac {x^{3}}{9}\right ) \Gamma \left (\frac {2}{3}\right )^{2} \left (3^{\frac {1}{6}} \operatorname {AiryBi}\left (x \right )+3^{\frac {2}{3}} \operatorname {AiryAi}\left (x \right )\right )\right ) x}{16 \Gamma \left (\frac {2}{3}\right )} \]
✓ Solution by Mathematica
Time used: 0.216 (sec). Leaf size: 142
DSolve[y''[x]-x*y[x]-x^6+64==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \, _0F_1\left (;\frac {4}{3};\frac {x^3}{9}\right ) \left (\frac {1}{7} x^8 \, _1F_2\left (\frac {7}{3};\frac {2}{3},\frac {10}{3};\frac {x^3}{9}\right )-64 x^2 \, _1F_2\left (\frac {1}{3};\frac {2}{3},\frac {4}{3};\frac {x^3}{9}\right )\right )+\, _0F_1\left (;\frac {2}{3};\frac {x^3}{9}\right ) \left (32 x^2 \, _1F_2\left (\frac {2}{3};\frac {4}{3},\frac {5}{3};\frac {x^3}{9}\right )-\frac {1}{8} x^8 \, _1F_2\left (\frac {8}{3};\frac {4}{3},\frac {11}{3};\frac {x^3}{9}\right )\right )+c_1 \operatorname {AiryAi}(x)+c_2 \operatorname {AiryBi}(x) \\ \end{align*}