Internal problem ID [8422]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, Additional non-linear first order
Problem number: 842.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_Riccati]
Solve \begin {gather*} \boxed {y^{\prime }-\frac {y+\ln \relax (x )^{3} x^{2}+2 x^{2} \ln \relax (x )^{2} y+y^{2} \ln \relax (x ) x^{2}}{x \ln \relax (x )}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 43
dsolve(diff(y(x),x) = (y(x)+x^2*ln(x)^3+2*x^2*ln(x)^2*y(x)+x^2*ln(x)*y(x)^2)/x/ln(x),y(x), singsol=all)
\[ y \relax (x ) = -\frac {\ln \relax (x ) \left (2 x^{2} \ln \relax (x )-x^{2}+2 c_{1}+4\right )}{2 x^{2} \ln \relax (x )-x^{2}+2 c_{1}} \]
✓ Solution by Mathematica
Time used: 0.368 (sec). Leaf size: 52
DSolve[y'[x] == (x^2*Log[x]^3 + y[x] + 2*x^2*Log[x]^2*y[x] + x^2*Log[x]*y[x]^2)/(x*Log[x]),y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {\log (x) \left (x^2-2 x^2 \log (x)-4 (1+c_1)\right )}{-x^2+2 x^2 \log (x)+4 c_1} \\ y(x)\to -\log (x) \\ \end{align*}