Internal problem ID [9054]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, Additional non-linear first order
Problem number: 719.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_Bernoulli]
\[ \boxed {y^{\prime }-\frac {y \left (-{\mathrm e}^{x}+\ln \left (2 x \right ) x^{2} y-\ln \left (2 x \right ) x \right ) {\mathrm e}^{-x}}{x}=0} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 36
dsolve(diff(y(x),x) = y(x)*(-exp(x)+ln(2*x)*x^2*y(x)-ln(2*x)*x)/x/exp(x),y(x), singsol=all)
\[ y \left (x \right ) = \frac {1}{x \left (1+2^{-{\mathrm e}^{-x}} x^{-{\mathrm e}^{-x}} {\mathrm e}^{-\operatorname {expIntegral}_{1}\left (x \right )} c_{1} \right )} \]
✓ Solution by Mathematica
Time used: 0.773 (sec). Leaf size: 49
DSolve[y'[x] == (y[x]*(-E^x - x*Log[2*x] + x^2*Log[2*x]*y[x]))/(E^x*x),y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {2^{e^{-x}}}{x \left (2^{e^{-x}}+c_1 x^{-e^{-x}} e^{\operatorname {ExpIntegralEi}(-x)}\right )} \\ y(x)\to 0 \\ \end{align*}