Internal problem ID [7700]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, linear first order
Problem number: 120.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_1st_order, _with_symmetry_[F(x),G(y)]]]
Solve \begin {gather*} \boxed {y^{\prime } x -y \left (x \ln \left (\frac {x^{2}}{y}\right )+2\right )=0} \end {gather*}
✓ Solution by Maple
Time used: 0.013 (sec). Leaf size: 17
dsolve(x*diff(y(x),x) - y(x)*(x*ln(x^2/y(x))+2)=0,y(x), singsol=all)
\[ y \relax (x ) = x^{2} {\mathrm e}^{-{\mathrm e}^{-x} c_{1}} \]
✓ Solution by Mathematica
Time used: 0.296 (sec). Leaf size: 20
DSolve[x*y'[x] - y[x]*(x*Log[x^2/y[x]]+2)==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to x^2 e^{-2 c_1 e^{-x}} \\ \end{align*}