Internal problem ID [6432]
Book: Own collection of miscellaneous problems
Section: section 2.0
Problem number: 48.
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^{2} y-x^{3}-\frac {1}{x}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 24
dsolve(diff(y(x),x$2)-1/x*diff(y(x),x)-x^2*y(x)-x^3-1/x=0,y(x), singsol=all)
\[ y \relax (x ) = \sinh \left (\frac {x^{2}}{2}\right ) c_{2}+\cosh \left (\frac {x^{2}}{2}\right ) c_{1}-x \]
✓ Solution by Mathematica
Time used: 0.059 (sec). Leaf size: 34
DSolve[y''[x]-1/x*y'[x]-x^2*y[x]-x^3-1/x==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to c_1 \cosh \left (\frac {x^2}{2}\right )+i c_2 \sinh \left (\frac {x^2}{2}\right )-x \\ \end{align*}