Internal problem ID [9271]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, Additional non-linear first order
Problem number: 936.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_1st_order, _with_linear_symmetries], _Abel]
\[ \boxed {y^{\prime }-y^{2}-\frac {7 x^{2} y}{16}+\frac {y x}{2}-y^{3}-\frac {3 y^{2} x^{2}}{8}+\frac {3 x y^{2}}{4}-\frac {3 x^{4} y}{64}+\frac {3 y x^{3}}{16}=-\frac {1}{4} x +1+\frac {5}{128} x^{4}-\frac {5}{64} x^{3}+\frac {1}{16} x^{2}+\frac {1}{512} x^{6}-\frac {3}{256} x^{5}} \]
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 39
dsolve(diff(y(x),x) = -1/4*x+1+y(x)^2+7/16*x^2*y(x)-1/2*x*y(x)+5/128*x^4-5/64*x^3+1/16*x^2+y(x)^3+3/8*x^2*y(x)^2-3/4*x*y(x)^2+3/64*y(x)*x^4-3/16*x^3*y(x)+1/512*x^6-3/256*x^5,y(x), singsol=all)
\[ y \left (x \right ) = -\frac {x^{2}}{8}+\frac {x}{4}+\operatorname {RootOf}\left (-x +4 \left (\int _{}^{\textit {\_Z}}\frac {1}{4 \textit {\_a}^{3}+4 \textit {\_a}^{2}+3}d \textit {\_a} \right )+c_{1} \right ) \]
✓ Solution by Mathematica
Time used: 0.194 (sec). Leaf size: 99
DSolve[y'[x] == 1 - x/4 + x^2/16 - (5*x^3)/64 + (5*x^4)/128 - (3*x^5)/256 + x^6/512 - (x*y[x])/2 + (7*x^2*y[x])/16 - (3*x^3*y[x])/16 + (3*x^4*y[x])/64 + y[x]^2 - (3*x*y[x]^2)/4 + (3*x^2*y[x]^2)/8 + y[x]^3,y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [-\frac {89}{3} \text {RootSum}\left [-89 \text {$\#$1}^3+6 \sqrt [3]{178} \text {$\#$1}-89\&,\frac {\log \left (\frac {2^{2/3} \left (\frac {1}{8} \left (3 x^2-6 x+8\right )+3 y(x)\right )}{\sqrt [3]{89}}-\text {$\#$1}\right )}{2 \sqrt [3]{178}-89 \text {$\#$1}^2}\&\right ]=\frac {89^{2/3} x}{18 \sqrt [3]{2}}+c_1,y(x)\right ] \]