Internal problem ID [8261]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, Additional non-linear first order
Problem number: 681.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class D], _Riccati]
Solve \begin {gather*} \boxed {y^{\prime }-\frac {y+x^{3} b \ln \left (\frac {1}{x}\right )+x^{4} b +b \,x^{3}+x a y^{2} \ln \left (\frac {1}{x}\right )+y^{2} a \,x^{2}+a x y^{2}}{x}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.022 (sec). Leaf size: 57
dsolve(diff(y(x),x) = (y(x)+x^3*b*ln(1/x)+x^4*b+b*x^3+x*a*y(x)^2*ln(1/x)+x^2*a*y(x)^2+a*x*y(x)^2)/x,y(x), singsol=all)
\[ y \relax (x ) = \frac {\tan \left (\frac {x^{2} \ln \left (\frac {1}{x}\right ) \sqrt {a b}}{2}+\frac {x^{3} \sqrt {a b}}{3}+\frac {3 \sqrt {a b}\, x^{2}}{4}+c_{1} \sqrt {a b}\right ) x \sqrt {a b}}{a} \]
✓ Solution by Mathematica
Time used: 29.113 (sec). Leaf size: 53
DSolve[y'[x] == (b*x^3 + b*x^4 + b*x^3*Log[x^(-1)] + y[x] + a*x*y[x]^2 + a*x^2*y[x]^2 + a*x*Log[x^(-1)]*y[x]^2)/x,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {\sqrt {b} x \tan \left (\frac {1}{12} \sqrt {a} \sqrt {b} \left ((4 x+9) x^2-6 x^2 \log (x)+12 c_1\right )\right )}{\sqrt {a}} \\ \end{align*}