Internal problem ID [6431]
Book: Own collection of miscellaneous problems
Section: section 2.0
Problem number: 47.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {y^{\prime \prime }-\frac {y^{\prime }}{x}-x y-x^{2}-\frac {1}{x}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.005 (sec). Leaf size: 28
dsolve(diff(y(x),x$2)-1/x*diff(y(x),x)-x*y(x)-x^2-1/x=0,y(x), singsol=all)
\[ y \relax (x ) = x \BesselI \left (\frac {2}{3}, \frac {2 x^{\frac {3}{2}}}{3}\right ) c_{2}+x \BesselK \left (\frac {2}{3}, \frac {2 x^{\frac {3}{2}}}{3}\right ) c_{1}-x \]
✓ Solution by Mathematica
Time used: 0.193 (sec). Leaf size: 138
DSolve[y''[x]-1/x*y'[x]-x*y[x]-x^2-1/x==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{4} x \, _0F_1\left (;\frac {5}{3};\frac {x^3}{9}\right ) \left (x^3 \, _1F_2\left (\frac {2}{3};\frac {1}{3},\frac {5}{3};\frac {x^3}{9}\right )-2 \, _1F_2\left (-\frac {1}{3};\frac {1}{3},\frac {2}{3};\frac {x^3}{9}\right )\right )-\frac {1}{8} x \, _0F_1\left (;\frac {1}{3};\frac {x^3}{9}\right ) \left (x^3 \, _1F_2\left (\frac {4}{3};\frac {5}{3},\frac {7}{3};\frac {x^3}{9}\right )+4 \, _1F_2\left (\frac {1}{3};\frac {4}{3},\frac {5}{3};\frac {x^3}{9}\right )\right )+c_1 \text {Ai}'(x)+c_2 \text {Bi}'(x) \\ \end{align*}