Internal problem ID [8479]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, Additional non-linear first order
Problem number: 901.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [NONE]
\[ \boxed {y^{\prime }-\frac {\left (y-a \ln \left (y\right ) x +x^{2}\right ) y}{\left (-y \ln \left (y\right )-\ln \left (x \right ) y-y+a x \right ) x}=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 31
dsolve(diff(y(x),x) = (y(x)-a*ln(y(x))*x+x^2)/(-y(x)*ln(y(x))-y(x)*ln(x)-y(x)+a*x)*y(x)/x,y(x), singsol=all)
\[ y \left (x \right ) = {\mathrm e}^{\operatorname {RootOf}\left (2 a x \textit {\_Z} -2 \,{\mathrm e}^{\textit {\_Z}} \ln \left (x \right )-2 \textit {\_Z} \,{\mathrm e}^{\textit {\_Z}}-x^{2}+2 c_{1} \right )} \]
✓ Solution by Mathematica
Time used: 0.447 (sec). Leaf size: 33
DSolve[y'[x] == (y[x]*(x^2 - a*x*Log[y[x]] + y[x]))/(x*(a*x - y[x] - Log[x]*y[x] - Log[y[x]]*y[x])),y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [a x \log (y(x))-\frac {x^2}{2}-y(x) \log (x)-y(x) \log (y(x))=c_1,y(x)\right ] \]