60.2.235 problem 811

Internal problem ID [10822]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, Additional non-linear first order
Problem number : 811
Date solved : Tuesday, January 28, 2025 at 05:17:27 PM
CAS classification : [`y=_G(x,y')`]

\begin{align*} y^{\prime }&=\frac {x^{3} {\mathrm e}^{y}+x^{4}+{\mathrm e}^{y} y-{\mathrm e}^{y} \ln \left ({\mathrm e}^{y}+x \right )+y x -\ln \left ({\mathrm e}^{y}+x \right ) x +x}{x^{2}} \end{align*}

✓ Solution by Maple

Time used: 0.119 (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)
 

\[ y = \frac {x^{3}}{2}+c_{1} x +\ln \left (-\frac {x}{-1+{\mathrm e}^{\frac {x \left (x^{2}+2 c_{1} \right )}{2}}}\right ) \]

✓ Solution by Mathematica

Time used: 3.068 (sec). Leaf size: 29

DSolve[D[y[x],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]
 

\[ y(x)\to -\log \left (\frac {-1+e^{-\frac {1}{2} x \left (x^2+2 c_1\right )}}{x}\right ) \]