Internal problem ID [8391]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, Additional non-linear first order
Problem number: 811.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [y=_G(x,y')]
Solve \begin {gather*} \boxed {y^{\prime }-\frac {x^{3} {\mathrm e}^{y}+x^{4}+{\mathrm e}^{y} y-{\mathrm e}^{y} \ln \left ({\mathrm e}^{y}+x \right )+x y-\ln \left ({\mathrm e}^{y}+x \right ) x +x}{x^{2}}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.226 (sec). Leaf size: 32
dsolve(diff(y(x),x) = (x^3*exp(y(x))+x^4+exp(y(x))*y(x)-exp(y(x))*ln(exp(y(x))+x)+x*y(x)-ln(exp(y(x))+x)*x+x)/x^2,y(x), singsol=all)
\[ y \relax (x ) = \frac {x^{3}}{2}+c_{1} x +\ln \left (-\frac {x}{-1+{\mathrm e}^{\frac {x^{3}}{2}} {\mathrm e}^{c_{1} x}}\right ) \]
✓ Solution by Mathematica
Time used: 4.083 (sec). Leaf size: 29
DSolve[y'[x] == (x + E^y[x]*x^3 + x^4 - E^y[x]*Log[E^y[x] + x] - x*Log[E^y[x] + x] + E^y[x]*y[x] + x*y[x])/x^2,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\log \left (\frac {-1+e^{-\frac {1}{2} x \left (x^2+2 c_1\right )}}{x}\right ) \\ \end{align*}