Internal problem ID [8282]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, Additional non-linear first order
Problem number: 702.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class D], _Riccati]
Solve \begin {gather*} \boxed {y^{\prime }-\frac {-y \,{\mathrm e}^{x}+y x -x^{3} \ln \relax (x )-x^{3}-x y^{2} \ln \relax (x )-y^{2} x}{\left (-{\mathrm e}^{x}+x \right ) x}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.038 (sec). Leaf size: 35
dsolve(diff(y(x),x) = (-y(x)*exp(x)+x*y(x)-x^3*ln(x)-x^3-x*y(x)^2*ln(x)-x*y(x)^2)/(-exp(x)+x)/x,y(x), singsol=all)
\[ y \relax (x ) = \tan \left (\int \frac {x \ln \relax (x )}{-x +{\mathrm e}^{x}}d x +\int \frac {x}{-x +{\mathrm e}^{x}}d x +c_{1}\right ) x \]
✓ Solution by Mathematica
Time used: 5.709 (sec). Leaf size: 37
DSolve[y'[x] == (-x^3 - x^3*Log[x] - E^x*y[x] + x*y[x] - x*y[x]^2 - x*Log[x]*y[x]^2)/(x*(-E^x + x)),y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to x \tan \left (\int _1^x\frac {K[1] (\log (K[1])+1)}{e^{K[1]}-K[1]}dK[1]+c_1\right ) \\ \end{align*}