60.2.294 problem 871

Internal problem ID [10881]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, Additional non-linear first order
Problem number : 871
Date solved : Monday, January 27, 2025 at 10:20:24 PM
CAS classification : [[_1st_order, `_with_symmetry_[F(x),G(x)]`], _Riccati]

\begin{align*} y^{\prime }&=\frac {2 x y^{2}+4 y \ln \left (2 x +1\right ) x +2 \ln \left (2 x +1\right )^{2} x +y^{2}-2+\ln \left (2 x +1\right )^{2}+2 y \ln \left (2 x +1\right )}{2 x +1} \end{align*}

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 26

dsolve(diff(y(x),x) = 1/(2*x+1)*(2*x*y(x)^2+4*y(x)*ln(2*x+1)*x+2*ln(2*x+1)^2*x+y(x)^2-2+ln(2*x+1)^2+2*y(x)*ln(2*x+1)),y(x), singsol=all)
 

\[ y = \frac {-1+\left (-x +c_{1} \right ) \ln \left (2 x +1\right )}{x -c_{1}} \]

✓ Solution by Mathematica

Time used: 0.439 (sec). Leaf size: 34

DSolve[D[y[x],x] == (-2 + Log[1 + 2*x]^2 + 2*x*Log[1 + 2*x]^2 + 2*Log[1 + 2*x]*y[x] + 4*x*Log[1 + 2*x]*y[x] + y[x]^2 + 2*x*y[x]^2)/(1 + 2*x),y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to -\log (2 x+1)+\frac {1}{-x+c_1} \\ y(x)\to -\log (2 x+1) \\ \end{align*}