Internal problem ID [7925]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, linear first order
Problem number: 345.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_1st_order, _with_symmetry_[F(x)*G(y),0]]]
Solve \begin {gather*} \boxed {x \left (2 x^{2} y \ln \relax (y)+1\right ) y^{\prime }-2 y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.172 (sec). Leaf size: 36
dsolve(x*(2*x^2*y(x)*ln(y(x))+1)*diff(y(x),x)-2*y(x) = 0,y(x), singsol=all)
\[ y \relax (x ) = {\mathrm e}^{\RootOf \left (2 \textit {\_Z} \,{\mathrm e}^{2 \textit {\_Z}} x^{2}-{\mathrm e}^{2 \textit {\_Z}} x^{2}+2 c_{1} x^{2}+2 \,{\mathrm e}^{\textit {\_Z}}\right )} \]
✓ Solution by Mathematica
Time used: 0.168 (sec). Leaf size: 35
DSolve[-2*y[x] + x*(1 + 2*x^2*Log[y[x]]*y[x])*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [\frac {y(x)}{x^2}+2 \left (\frac {1}{2} y(x)^2 \log (y(x))-\frac {y(x)^2}{4}\right )=c_1,y(x)\right ] \]