Internal problem ID [9320]
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]
\[ \boxed {y^{\prime }-\frac {y^{3}-3 x y^{2} \ln \left (x \right )+3 x^{2} \ln \left (x \right )^{2} y-x^{3} \ln \left (x \right )^{3}+x^{2}+x y}{x^{2}}=0} \]
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 33
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 ) &= x \left (-\frac {1}{\sqrt {-2 x +c_{1}}}+\ln \left (x \right )\right ) \\ y \left (x \right ) &= x \left (\frac {1}{\sqrt {-2 x +c_{1}}}+\ln \left (x \right )\right ) \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.25 (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*}