Internal problem ID [6423]
Book: Own collection of miscellaneous problems
Section: section 2.0
Problem number: 39.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {y^{\prime \prime }-y x^{3}-x^{3}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.009 (sec). Leaf size: 30
dsolve(diff(y(x),x$2)-x^3*y(x)-x^3=0,y(x), singsol=all)
\[ y \relax (x ) = \sqrt {x}\, \BesselI \left (\frac {1}{5}, \frac {2 x^{\frac {5}{2}}}{5}\right ) c_{2}+\sqrt {x}\, \BesselK \left (\frac {1}{5}, \frac {2 x^{\frac {5}{2}}}{5}\right ) c_{1}-1 \]
✓ Solution by Mathematica
Time used: 0.117 (sec). Leaf size: 85
DSolve[y''[x]-x^3*y[x]-x^3==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {\pi c_2 \sqrt {x} I_{\frac {1}{5}}\left (\frac {2 x^{5/2}}{5}\right ) \text {Root}\left [\text {$\#$1}^{20}-25600 \text {$\#$1}^{10}+5242880\&,5\right ]}{\sqrt {5} \text {Gamma}\left (-\frac {1}{5}\right )}+\left (1+\frac {c_1 \left (x^{5/2}\right )^{4/5}}{x^2}\right ) \, _0F_1\left (;\frac {4}{5};\frac {x^5}{25}\right )-1 \\ \end{align*}