60.2.381 problem 958

Internal problem ID [10968]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, Additional non-linear first order
Problem number : 958
Date solved : Tuesday, January 28, 2025 at 05:39:55 PM
CAS classification : [[_1st_order, `_with_symmetry_[F(x),G(x)]`], _Abel]

\begin{align*} y^{\prime }&=\frac {2 x +4 y \ln \left (2 x +1\right ) x +6 y^{2} \ln \left (2 x +1\right ) x +6 y \ln \left (2 x +1\right )^{2} x +2 \ln \left (2 x +1\right )^{3} x +2 x y^{3}+2 \ln \left (2 x +1\right )^{2} x +2 x y^{2}-1+3 y^{2} \ln \left (2 x +1\right )+3 y \ln \left (2 x +1\right )^{2}+y^{2}+y^{3}+2 y \ln \left (2 x +1\right )+\ln \left (2 x +1\right )^{2}+\ln \left (2 x +1\right )^{3}}{2 x +1} \end{align*}

✓ Solution by Maple

Time used: 0.006 (sec). Leaf size: 40

dsolve(diff(y(x),x) = 1/(2*x+1)*(2*x+4*y(x)*ln(2*x+1)*x+6*y(x)^2*ln(2*x+1)*x+6*y(x)*ln(2*x+1)^2*x+2*ln(2*x+1)^3*x+2*x*y(x)^3+2*ln(2*x+1)^2*x+2*x*y(x)^2-1+3*y(x)^2*ln(2*x+1)+3*y(x)*ln(2*x+1)^2+y(x)^2+y(x)^3+2*y(x)*ln(2*x+1)+ln(2*x+1)^2+ln(2*x+1)^3),y(x), singsol=all)
 

\[ y = -\ln \left (2 x +1\right )-\frac {1}{3}+\frac {29 \operatorname {RootOf}\left (-81 \left (\int _{}^{\textit {\_Z}}\frac {1}{841 \textit {\_a}^{3}-27 \textit {\_a} +27}d \textit {\_a} \right )+x +3 c_{1} \right )}{9} \]

✓ Solution by Mathematica

Time used: 0.326 (sec). Leaf size: 60

DSolve[D[y[x],x] == (-1 + 2*x + Log[1 + 2*x]^2 + 2*x*Log[1 + 2*x]^2 + Log[1 + 2*x]^3 + 2*x*Log[1 + 2*x]^3 + 2*Log[1 + 2*x]*y[x] + 4*x*Log[1 + 2*x]*y[x] + 3*Log[1 + 2*x]^2*y[x] + 6*x*Log[1 + 2*x]^2*y[x] + y[x]^2 + 2*x*y[x]^2 + 3*Log[1 + 2*x]*y[x]^2 + 6*x*Log[1 + 2*x]*y[x]^2 + y[x]^3 + 2*x*y[x]^3)/(1 + 2*x),y[x],x,IncludeSingularSolutions -> True]
 

\[ \text {Solve}\left [\int _1^{\frac {3 \log (2 x+1)+3 y(x)+1}{\sqrt [3]{29}}}\frac {1}{K[1]^3-\frac {3 K[1]}{29^{2/3}}+1}dK[1]=\frac {1}{9} 29^{2/3} x+c_1,y(x)\right ] \]