Internal problem ID [8574]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, Additional non-linear first order
Problem number: 994.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_Riccati]
Solve \begin {gather*} \boxed {y^{\prime }+x^{3} \left (-y^{2}-2 y \ln \relax (x )-\ln \relax (x )^{2}\right )-\frac {y}{\ln \relax (x ) x}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 43
dsolve(diff(y(x),x) = -x^3*(-y(x)^2-2*y(x)*ln(x)-ln(x)^2)+1/ln(x)/x*y(x),y(x), singsol=all)
\[ y \relax (x ) = -\frac {\ln \relax (x ) \left (4 x^{4} \ln \relax (x )-x^{4}+8 c_{1}+16\right )}{4 x^{4} \ln \relax (x )-x^{4}+8 c_{1}} \]
✓ Solution by Mathematica
Time used: 0.379 (sec). Leaf size: 52
DSolve[y'[x] == y[x]/(x*Log[x]) - x^3*(-Log[x]^2 - 2*Log[x]*y[x] - y[x]^2),y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {\log (x) \left (x^4-4 x^4 \log (x)-16 (1+c_1)\right )}{-x^4+4 x^4 \log (x)+16 c_1} \\ y(x)\to -\log (x) \\ \end{align*}