Internal problem ID [8434]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, Additional non-linear first order
Problem number: 854.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [NONE]
Solve \begin {gather*} \boxed {y^{\prime }-\frac {y \left (\ln \relax (x )+\ln \relax (y)-1+x^{2} \ln \relax (x )^{2}+2 x^{2} \ln \relax (y) \ln \relax (x )+x^{2} \ln \relax (y)^{2}\right )}{x}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 51
dsolve(diff(y(x),x) = y(x)*(ln(x)+ln(y(x))-1+x^2*ln(x)^2+2*x^2*ln(y(x))*ln(x)+x^2*ln(y(x))^2)/x,y(x), singsol=all)
\[ y \relax (x ) = x^{-\frac {x^{3}}{x^{3}+3 c_{1}}} x^{-\frac {3 c_{1}}{x^{3}+3 c_{1}}} {\mathrm e}^{-\frac {3 x}{x^{3}+3 c_{1}}} \]
✓ Solution by Mathematica
Time used: 0.328 (sec). Leaf size: 31
DSolve[y'[x] == ((-1 + Log[x] + x^2*Log[x]^2 + Log[y[x]] + 2*x^2*Log[x]*Log[y[x]] + x^2*Log[y[x]]^2)*y[x])/x,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {e^{-\frac {3 x}{x^3+3 c_1}}}{x} \\ y(x)\to \frac {1}{x} \\ \end{align*}