Internal problem ID [8257]
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]
Solve \begin {gather*} \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} \end {gather*}
✓ Solution by Maple
Time used: 0.006 (sec). Leaf size: 64
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)
\[ y \relax (x ) = \tanh \left (\frac {\ln \left (x +1\right ) \sqrt {a}\, x^{2}}{2}+\frac {x^{3} \sqrt {a}}{3}+\frac {\sqrt {a}\, x^{2}}{4}-\frac {\sqrt {a}\, \ln \left (x +1\right )}{2}+c_{1} \sqrt {a}+\frac {\sqrt {a}\, x}{2}+\frac {3 \sqrt {a}}{4}\right ) x \sqrt {a} \]
✓ Solution by Mathematica
Time used: 5.722 (sec). Leaf size: 49
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]
\begin{align*} y(x)\to \sqrt {a} x \tanh \left (\frac {1}{12} \sqrt {a} \left (6 \left (x^2-1\right ) \log (x+1)+x (x (4 x+3)+6)+12 c_1\right )\right ) \\ \end{align*}