Internal problem ID [8573]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, Additional non-linear first order
Problem number: 993.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_Riccati]
Solve \begin {gather*} \boxed {y^{\prime }+F \relax (x ) \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: 0.004 (sec). Leaf size: 35
dsolve(diff(y(x),x) = -F(x)*(-y(x)^2-2*y(x)*ln(x)-ln(x)^2)+1/ln(x)/x*y(x),y(x), singsol=all)
\[ y \relax (x ) = -\frac {\ln \relax (x ) \left (\int -2 \ln \relax (x ) F \relax (x )d x -c_{1}-2\right )}{\int -2 \ln \relax (x ) F \relax (x )d x -c_{1}} \]
✓ Solution by Mathematica
Time used: 2.951 (sec). Leaf size: 75
DSolve[y'[x] == y[x]/(x*Log[x]) - F[x]*(-Log[x]^2 - 2*Log[x]*y[x] - y[x]^2),y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {\int _1^x\frac {F(K[5])}{\sqrt {\frac {1}{\log ^2(K[5])}}}dK[5]-1+c_1}{\sqrt {\frac {1}{\log ^2(x)}} \left (\int _1^x\frac {F(K[5])}{\sqrt {\frac {1}{\log ^2(K[5])}}}dK[5]+c_1\right )} \\ y(x)\to \frac {1}{\sqrt {\frac {1}{\log ^2(x)}}} \\ \end{align*}