Internal problem ID [8514]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, Additional non-linear first order
Problem number: 934.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_1st_order, _with_linear_symmetries], _Abel]
Solve \begin {gather*} \boxed {y^{\prime }-\frac {x}{2}-1-y^{2}-\frac {y x^{2}}{4}+y x +\frac {x^{4}}{8}-\frac {x^{3}}{8}-\frac {x^{2}}{4}-y^{3}+\frac {3 y^{2} x^{2}}{4}+\frac {3 x y^{2}}{2}-\frac {3 y x^{4}}{16}-\frac {3 y x^{3}}{4}+\frac {x^{6}}{64}+\frac {3 x^{5}}{32}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 39
dsolve(diff(y(x),x) = 1/2*x+1+y(x)^2+1/4*x^2*y(x)-x*y(x)-1/8*x^4+1/8*x^3+1/4*x^2+y(x)^3-3/4*x^2*y(x)^2-3/2*x*y(x)^2+3/16*y(x)*x^4+3/4*x^3*y(x)-1/64*x^6-3/32*x^5,y(x), singsol=all)
\[ y \relax (x ) = \frac {x^{2}}{4}+\frac {x}{2}+\RootOf \left (-x +2 \left (\int _{}^{\textit {\_Z}}\frac {1}{2 \textit {\_a}^{3}+2 \textit {\_a}^{2}+1}d \textit {\_a} \right )+c_{1}\right ) \]
✓ Solution by Mathematica
Time used: 0.201 (sec). Leaf size: 102
DSolve[y'[x] == 1 + x/2 + x^2/4 + x^3/8 - x^4/8 - (3*x^5)/32 - x^6/64 - x*y[x] + (x^2*y[x])/4 + (3*x^3*y[x])/4 + (3*x^4*y[x])/16 + y[x]^2 - (3*x*y[x]^2)/2 - (3*x^2*y[x]^2)/4 + y[x]^3,y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [-\frac {31}{3} \text {RootSum}\left [-31 \text {$\#$1}^3+3\ 2^{2/3} \sqrt [3]{31} \text {$\#$1}-31\&,\frac {\log \left (\sqrt [3]{\frac {2}{31}} \left (\frac {1}{4} \left (-3 x^2-6 x+4\right )+3 y(x)\right )-\text {$\#$1}\right )}{2^{2/3} \sqrt [3]{31}-31 \text {$\#$1}^2}\&\right ]=\frac {1}{9} \left (\frac {31}{2}\right )^{2/3} x+c_1,y(x)\right ] \]