60.2.234 problem 810

Internal problem ID [10821]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, Additional non-linear first order
Problem number : 810
Date solved : Monday, January 27, 2025 at 10:06:23 PM
CAS classification : [[_1st_order, `_with_symmetry_[F(x),G(x)]`], _Riccati]

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

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 16

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

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

✓ Solution by Mathematica

Time used: 0.207 (sec). Leaf size: 26

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

\begin{align*} y(x)\to x \left (\log (x)+\frac {1}{-x+c_1}\right ) \\ y(x)\to x \log (x) \\ \end{align*}