Internal problem ID [8299]
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]
Solve \begin {gather*} \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} \end {gather*}
✓ Solution by Maple
Time used: 0.038 (sec). Leaf size: 34
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)
\[ y \relax (x ) = \frac {1}{2^{-{\mathrm e}^{-x}} x^{-{\mathrm e}^{-x}+1} c_{1} {\mathrm e}^{-\expIntegral \left (1, x\right )}+x} \]
✓ Solution by Mathematica
Time used: 0.611 (sec). Leaf size: 42
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 {1}{x+c_1 e^{\text {ExpIntegralEi}(-x)} 2^{\sinh (x)-\cosh (x)} x^{\sinh (x)-\cosh (x)+1}} \\ y(x)\to 0 \\ \end{align*}