Internal problem ID [8564]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, Additional non-linear first order
Problem number: 986.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_Abel]
\[ \boxed {y^{\prime }-\frac {y^{3}-3 x y^{2} \ln \left (x \right )+3 \ln \left (x \right )^{2} y x^{2}-\ln \left (x \right )^{3} x^{3}+x^{2}+y x}{x^{2}}=0} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 36
dsolve(diff(y(x),x) = (y(x)^3-3*x*y(x)^2*ln(x)+3*x^2*ln(x)^2*y(x)-x^3*ln(x)^3+x^2+x*y(x))/x^2,y(x), singsol=all)
\begin{align*} y \left (x \right ) = -\frac {x}{\sqrt {-2 x +c_{1}}}+\ln \left (x \right ) x \\ y \left (x \right ) = \frac {x}{\sqrt {-2 x +c_{1}}}+\ln \left (x \right ) x \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.255 (sec). Leaf size: 49
DSolve[y'[x] == (x^2 - x^3*Log[x]^3 + x*y[x] + 3*x^2*Log[x]^2*y[x] - 3*x*Log[x]*y[x]^2 + y[x]^3)/x^2,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to x \left (\log (x)-\frac {1}{\sqrt {-2 x+c_1}}\right ) \\ y(x)\to x \left (\log (x)+\frac {1}{\sqrt {-2 x+c_1}}\right ) \\ y(x)\to x \log (x) \\ \end{align*}