Internal problem ID [6411]
Book: Own collection of miscellaneous problems
Section: section 2.0
Problem number: 28.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime }-y x -x^{3}+2=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 18
dsolve(diff(y(x),x$2)-x*y(x)-x^3+2=0,y(x), singsol=all)
\[ y \left (x \right ) = \operatorname {AiryAi}\left (x \right ) c_{2} +\operatorname {AiryBi}\left (x \right ) c_{1} -x^{2} \]
✓ Solution by Mathematica
Time used: 0.207 (sec). Leaf size: 141
DSolve[y''[x]-x*y[x]-x^3+2==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{4} \, _0F_1\left (;\frac {4}{3};\frac {x^3}{9}\right ) \left (x^5 \, _1F_2\left (\frac {4}{3};\frac {2}{3},\frac {7}{3};\frac {x^3}{9}\right )-8 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 (x^2 \, _1F_2\left (\frac {2}{3};\frac {4}{3},\frac {5}{3};\frac {x^3}{9}\right )-\frac {1}{5} x^5 \, _1F_2\left (\frac {5}{3};\frac {4}{3},\frac {8}{3};\frac {x^3}{9}\right )\right )+c_1 \operatorname {AiryAi}(x)+c_2 \operatorname {AiryBi}(x) \\ \end{align*}