Internal problem ID [8538]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, Additional non-linear first order
Problem number: 958.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_1st_order, _with_symmetry_[F(x),G(x)]], _Abel]
Solve \begin {gather*} \boxed {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}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.004 (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)
\[ y \relax (x ) = -\ln \left (2 x +1\right )-\frac {1}{3}+\frac {29 \RootOf \left (-81 \left (\int _{}^{\textit {\_Z}}\frac {1}{841 \textit {\_a}^{3}-27 \textit {\_a} +27}d \textit {\_a} \right )+x +3 c_{1}\right )}{9} \]
✓ Solution by Mathematica
Time used: 0.311 (sec). Leaf size: 82
DSolve[y'[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]
\[ \text {Solve}\left [-\frac {29}{3} \text {RootSum}\left [-29 \text {$\#$1}^3+3 \sqrt [3]{29} \text {$\#$1}-29\&,\frac {\log \left (\frac {3 y(x)+3 \log (2 x+1)+1}{\sqrt [3]{29}}-\text {$\#$1}\right )}{\sqrt [3]{29}-29 \text {$\#$1}^2}\&\right ]=\frac {1}{9} 29^{2/3} x+c_1,y(x)\right ] \]