Internal problem ID [8388]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, Additional non-linear first order
Problem number: 810.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_1st_order, `_with_symmetry_[F(x),G(x)]`], _Riccati]
\[ \boxed {y^{\prime }-\frac {x +y+y^{2}-2 \ln \left (x \right ) y x +\ln \left (x \right )^{2} x^{2}}{x}=0} \]
✓ Solution by Maple
Time used: 0.0 (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)
\[ y \left (x \right ) = \left (\ln \left (x \right )+\frac {1}{-x +c_{1}}\right ) x \]
✓ Solution by Mathematica
Time used: 0.216 (sec). Leaf size: 26
DSolve[y'[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*}