60.2.293 problem 870

Internal problem ID [10880]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, Additional non-linear first order
Problem number : 870
Date solved : Tuesday, January 28, 2025 at 05:28:28 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+{\mathrm e}^{-\frac {y}{x}} x +x +x^{3}+x^{4}\right ) {\mathrm e}^{\frac {y}{x}}}{x} \end{align*}

✓ Solution by Maple

Time used: 0.012 (sec). Leaf size: 37

dsolve(diff(y(x),x) = (exp(-y(x)/x)*y(x)+exp(-y(x)/x)*x+x+x^3+x^4)*exp(y(x)/x)/x,y(x), singsol=all)
 

\[ y = \left (2 \ln \left (2\right )+\ln \left (3\right )-\ln \left (\frac {-3 x^{4}-4 x^{3}-12 c_{1} -12 x}{x}\right )\right ) x \]

✓ Solution by Mathematica

Time used: 3.498 (sec). Leaf size: 32

DSolve[D[y[x],x] == (E^(y[x]/x)*(x + x/E^(y[x]/x) + x^3 + x^4 + y[x]/E^(y[x]/x)))/x,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to -x \log \left (-\frac {x^3}{4}-\frac {x^2}{3}-\frac {c_1}{x}-1\right ) \]