Internal problem ID [8303]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, Additional non-linear first order
Problem number: 725.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_1st_order, `_with_symmetry_[F(x),G(x)]`], _Riccati]
\[ \boxed {y^{\prime }-\frac {-\ln \left (x \right )+2 y \ln \left (2 x \right ) x +\ln \left (2 x \right )+\ln \left (2 x \right ) y^{2}+\ln \left (2 x \right ) x^{2}}{\ln \left (x \right )}=0} \]
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 25
dsolve(diff(y(x),x) = (-ln(x)+2*ln(2*x)*x*y(x)+ln(2*x)+ln(2*x)*y(x)^2+ln(2*x)*x^2)/ln(x),y(x), singsol=all)
\[ y \left (x \right ) = -x -\tan \left (c_{1} +\ln \left (2\right ) \operatorname {Ei}_{1}\left (-\ln \left (x \right )\right )-x \right ) \]
✓ Solution by Mathematica
Time used: 0.714 (sec). Leaf size: 19
DSolve[y'[x] == (-Log[x] + Log[2*x] + x^2*Log[2*x] + 2*x*Log[2*x]*y[x] + Log[2*x]*y[x]^2)/Log[x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -x+\tan (\log (2) \operatorname {LogIntegral}(x)+x+c_1) \\ \end{align*}