60.2.351 problem 928

Internal problem ID [10938]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, Additional non-linear first order
Problem number : 928
Date solved : Tuesday, January 28, 2025 at 05:31:20 PM
CAS classification : [[_1st_order, `_with_symmetry_[F(x),G(x)*y+H(x)]`]]

\begin{align*} y^{\prime }&=\frac {\left ({\mathrm e}^{-\frac {y}{x}} y x +{\mathrm e}^{-\frac {y}{x}} y+{\mathrm e}^{-\frac {y}{x}} x^{2}+{\mathrm e}^{-\frac {y}{x}} x +x \right ) {\mathrm e}^{\frac {y}{x}}}{x \left (1+x \right )} \end{align*}

✓ Solution by Maple

Time used: 0.012 (sec). Leaf size: 20

dsolve(diff(y(x),x) = (exp(-y(x)/x)*y(x)*x+exp(-y(x)/x)*y(x)+exp(-y(x)/x)*x^2+exp(-y(x)/x)*x+x)*exp(y(x)/x)/x/(x+1),y(x), singsol=all)
 

\[ y = -\ln \left (\frac {-\ln \left (x +1\right )+c_{1}}{x}\right ) x \]

✓ Solution by Mathematica

Time used: 1.740 (sec). Leaf size: 22

DSolve[D[y[x],x] == (E^(y[x]/x)*(x + x/E^(y[x]/x) + x^2/E^(y[x]/x) + y[x]/E^(y[x]/x) + (x*y[x])/E^(y[x]/x)))/(x*(1 + x)),y[x],x,IncludeSingularSolutions -> True]
 

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