Internal problem ID [8284]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, Additional non-linear first order
Problem number: 704.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class D], _Riccati]
Solve \begin {gather*} \boxed {y^{\prime }-\frac {\ln \relax (x ) y x -y+2 x^{5} b +2 x^{3} a y^{2}}{\left (x \ln \relax (x )-1\right ) x}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.072 (sec). Leaf size: 45
dsolve(diff(y(x),x) = (y(x)*ln(x)*x-y(x)+2*x^5*b+2*x^3*a*y(x)^2)/(x*ln(x)-1)/x,y(x), singsol=all)
\[ y \relax (x ) = \frac {\tan \left (2 \left (\int \frac {x^{3}}{\ln \relax (x ) x -1}d x \right ) \sqrt {a b}+2 c_{1} \sqrt {a b}\right ) x \sqrt {a b}}{a} \]
✓ Solution by Mathematica
Time used: 52.255 (sec). Leaf size: 55
DSolve[y'[x] == (2*b*x^5 - y[x] + x*Log[x]*y[x] + 2*a*x^3*y[x]^2)/(x*(-1 + x*Log[x])),y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {\sqrt {b} x \tan \left (\sqrt {a} \sqrt {b} \left (\int _1^x\frac {2 K[1]^3}{K[1] \log (K[1])-1}dK[1]+c_1\right )\right )}{\sqrt {a}} \\ \end{align*}