Internal problem ID [9202]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, Additional non-linear first order
Problem number: 867.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_1st_order, _with_linear_symmetries], _Abel]
\[ \boxed {y^{\prime }-y^{2}-\frac {2 x^{2} y}{3}-y^{3}-y^{2} x^{2}-\frac {x^{4} y}{3}=-\frac {2}{3} x +1+\frac {1}{9} x^{4}+\frac {1}{27} x^{6}} \]
✓ Solution by Maple
Time used: 0.031 (sec). Leaf size: 30
dsolve(diff(y(x),x) = -2/3*x+1+y(x)^2+2/3*x^2*y(x)+1/9*x^4+y(x)^3+x^2*y(x)^2+1/3*y(x)*x^4+1/27*x^6,y(x), singsol=all)
\[ y \left (x \right ) = -\frac {x^{2}}{3}+\operatorname {RootOf}\left (-x +\int _{}^{\textit {\_Z}}\frac {1}{\textit {\_a}^{3}+\textit {\_a}^{2}+1}d \textit {\_a} +c_{1} \right ) \]
✓ Solution by Mathematica
Time used: 0.156 (sec). Leaf size: 77
DSolve[y'[x] == 1 - (2*x)/3 + x^4/9 + x^6/27 + (2*x^2*y[x])/3 + (x^4*y[x])/3 + y[x]^2 + x^2*y[x]^2 + y[x]^3,y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [-\frac {29}{3} \text {RootSum}\left [-29 \text {$\#$1}^3+3 \sqrt [3]{29} \text {$\#$1}-29\&,\frac {\log \left (\frac {x^2+3 y(x)+1}{\sqrt [3]{29}}-\text {$\#$1}\right )}{\sqrt [3]{29}-29 \text {$\#$1}^2}\&\right ]=\frac {1}{9} 29^{2/3} x+c_1,y(x)\right ] \]