Internal problem ID [9012]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, Additional non-linear first order
Problem number: 677.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class D`], _Riccati]
\[ \boxed {y^{\prime }-\frac {y+x^{3} a \ln \left (x +1\right )+a \,x^{4}+a \,x^{3}-x y^{2} \ln \left (x +1\right )-y^{2} x^{2}-y^{2} x}{x}=0} \]
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 48
dsolve(diff(y(x),x) = (y(x)+x^3*a*ln(x+1)+a*x^4+x^3*a-x*y(x)^2*ln(x+1)-x^2*y(x)^2-x*y(x)^2)/x,y(x), singsol=all)
\[ y \left (x \right ) = \tanh \left (\frac {\sqrt {a}\, \left (6 \ln \left (x +1\right ) x^{2}+4 x^{3}+3 x^{2}-6 \ln \left (x +1\right )+12 c_{1} +6 x +9\right )}{12}\right ) \sqrt {a}\, x \]
✓ Solution by Mathematica
Time used: 11.983 (sec). Leaf size: 51
DSolve[y'[x] == (a*x^3 + a*x^4 + a*x^3*Log[1 + x] + y[x] - x*y[x]^2 - x^2*y[x]^2 - x*Log[1 + x]*y[x]^2)/x,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \sqrt {a} x \tanh \left (\frac {1}{12} \sqrt {a} \left (4 x^3+3 x^2+6 \left (x^2-1\right ) \log (x+1)+6 x+12 c_1\right )\right ) \]