Internal problem ID [8889]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 2, linear second order
Problem number: 1310.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {x^{3} y^{\prime \prime }+3 x^{2} y^{\prime }+y x -1=0} \end {gather*}
✓ Solution by Maple
Time used: 0.002 (sec). Leaf size: 20
dsolve(x^3*diff(diff(y(x),x),x)+3*x^2*diff(y(x),x)+x*y(x)-1=0,y(x), singsol=all)
\[ y \relax (x ) = \frac {\ln \relax (x ) c_{1}+\frac {\ln \relax (x )^{2}}{2}+c_{2}}{x} \]
✓ Solution by Mathematica
Time used: 0.009 (sec). Leaf size: 27
DSolve[-1 + x*y[x] + 3*x^2*y'[x] + x^3*y''[x] == 0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {\log ^2(x)+2 c_2 \log (x)+2 c_1}{2 x} \\ \end{align*}