Internal problem ID [8746]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 2, linear second order
Problem number: 1166.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {y^{\prime \prime } x^{2}-x y^{\prime }+y-3 x^{3}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 18
dsolve(x^2*diff(diff(y(x),x),x)-x*diff(y(x),x)+y(x)-3*x^3=0,y(x), singsol=all)
\[ y \relax (x ) = x c_{2}+x \ln \relax (x ) c_{1}+\frac {3 x^{3}}{4} \]
✓ Solution by Mathematica
Time used: 0.008 (sec). Leaf size: 23
DSolve[-3*x^3 + y[x] - x*y'[x] + x^2*y''[x] == 0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {3 x^3}{4}+c_1 x+c_2 x \log (x) \\ \end{align*}