Internal problem ID [9016]
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]
\[ \boxed {y^{\prime }-\frac {y+x^{3} b \ln \left (\frac {1}{x}\right )+x^{4} b +b \,x^{3}+x a y^{2} \ln \left (\frac {1}{x}\right )+x^{2} a y^{2}+y^{2} a x}{x}=0} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 45
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)
\[ y \left (x \right ) = \frac {\tan \left (\frac {\left (6 x^{2} \ln \left (\frac {1}{x}\right )+4 x^{3}+9 x^{2}+12 c_{1} \right ) \sqrt {a b}}{12}\right ) x \sqrt {a b}}{a} \]
✓ Solution by Mathematica
Time used: 43.49 (sec). Leaf size: 54
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]
\[ y(x)\to \frac {\sqrt {b} x \tan \left (\frac {1}{12} \sqrt {a} \sqrt {b} \left (4 x^3+9 x^2-6 x^2 \log (x)+12 c_1\right )\right )}{\sqrt {a}} \]