Internal problem ID [8566]
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]
Solve \begin {gather*} \boxed {y^{\prime }-\frac {y^{3}-3 x y^{2} \ln \relax (x )+3 x^{2} \ln \relax (x )^{2} y-\ln \relax (x )^{3} x^{3}+x^{2}+y x}{x^{2}}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.002 (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 \relax (x ) = -\frac {x}{\sqrt {c_{1}-2 x}}+x \ln \relax (x ) \\ y \relax (x ) = \frac {x}{\sqrt {c_{1}-2 x}}+x \ln \relax (x ) \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.243 (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*}