Internal problem ID [7169]
Book: Own collection of miscellaneous problems
Section: section 2.0
Problem number: 32.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime }-y x=x^{3}} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 87
dsolve(diff(y(x),x$2)-x*y(x)-x^3=0,y(x), singsol=all)
\[ y \left (x \right ) = \frac {5 x^{4} \pi \operatorname {hypergeom}\left (\left [\frac {4}{3}\right ], \left [\frac {2}{3}, \frac {7}{3}\right ], \frac {x^{3}}{9}\right ) \left (\operatorname {AiryBi}\left (x \right ) 3^{\frac {1}{3}}-3^{\frac {5}{6}} \operatorname {AiryAi}\left (x \right )\right )-6 \Gamma \left (\frac {2}{3}\right ) \left (x^{5} \operatorname {hypergeom}\left (\left [\frac {5}{3}\right ], \left [\frac {4}{3}, \frac {8}{3}\right ], \frac {x^{3}}{9}\right ) \left (3^{\frac {1}{6}} \operatorname {AiryBi}\left (x \right )+3^{\frac {2}{3}} \operatorname {AiryAi}\left (x \right )\right ) \Gamma \left (\frac {2}{3}\right )-10 \operatorname {AiryBi}\left (x \right ) c_{1} -10 \operatorname {AiryAi}\left (x \right ) c_{2} \right )}{60 \Gamma \left (\frac {2}{3}\right )} \]
✓ Solution by Mathematica
Time used: 0.093 (sec). Leaf size: 137
DSolve[y''[x]-x*y[x]-x^3==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to -\frac {\pi x^5 \operatorname {Gamma}\left (\frac {5}{3}\right ) \left (3 \operatorname {AiryAi}(x)+\sqrt {3} \operatorname {AiryBi}(x)\right ) \, _1F_2\left (\frac {5}{3};\frac {4}{3},\frac {8}{3};\frac {x^3}{9}\right )}{9\ 3^{5/6} \operatorname {Gamma}\left (\frac {4}{3}\right ) \operatorname {Gamma}\left (\frac {8}{3}\right )}+\frac {\pi x^4 \operatorname {Gamma}\left (\frac {4}{3}\right ) \left (\operatorname {AiryBi}(x)-\sqrt {3} \operatorname {AiryAi}(x)\right ) \, _1F_2\left (\frac {4}{3};\frac {2}{3},\frac {7}{3};\frac {x^3}{9}\right )}{3\ 3^{2/3} \operatorname {Gamma}\left (\frac {2}{3}\right ) \operatorname {Gamma}\left (\frac {7}{3}\right )}+c_1 \operatorname {AiryAi}(x)+c_2 \operatorname {AiryBi}(x) \]