60.2.423 problem 1000

Internal problem ID [11010]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, Additional non-linear first order
Problem number : 1000
Date solved : Monday, January 27, 2025 at 10:41:20 PM
CAS classification : [_Riccati]

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

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 19

dsolve(diff(y(x),x) = 1/x^2*(2*x^2*y(x)+x^3+y(x)*ln(x)*x-y(x)^2-x*y(x))/(x+ln(x)),y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 1.103 (sec). Leaf size: 27

DSolve[D[y[x],x] == (x^3 - x*y[x] + 2*x^2*y[x] + x*Log[x]*y[x] - y[x]^2)/(x^2*(x + Log[x])),y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to \frac {x (x-c_1)}{\log (x)+c_1} \\ y(x)\to -x \\ \end{align*}