Internal problem ID [9270]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, Additional non-linear first order
Problem number: 935.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_1st_order, _with_linear_symmetries], _Abel]
\[ \boxed {y^{\prime }-y^{2}-\frac {7 x^{2} y}{2}+2 y x -y^{3}-\frac {3 y^{2} x^{2}}{4}+3 x y^{2}-\frac {3 x^{4} y}{16}+\frac {3 y x^{3}}{2}=-\frac {1}{2} x +1+\frac {13}{16} x^{4}-\frac {3}{2} x^{3}+x^{2}+\frac {1}{64} x^{6}-\frac {3}{16} x^{5}} \]
✓ Solution by Maple
Time used: 0.062 (sec). Leaf size: 55
dsolve(diff(y(x),x) = -1/2*x+1+y(x)^2+7/2*x^2*y(x)-2*x*y(x)+13/16*x^4-3/2*x^3+x^2+y(x)^3+3/4*x^2*y(x)^2-3*x*y(x)^2+3/16*y(x)*x^4-3/2*x^3*y(x)+1/64*x^6-3/16*x^5,y(x), singsol=all)
\[ y \left (x \right ) = \frac {{\mathrm e}^{\operatorname {RootOf}\left (\ln \left ({\mathrm e}^{\textit {\_Z}}-4\right ) {\mathrm e}^{\textit {\_Z}}+c_{1} {\mathrm e}^{\textit {\_Z}}-\textit {\_Z} \,{\mathrm e}^{\textit {\_Z}}+x \,{\mathrm e}^{\textit {\_Z}}-4 \ln \left ({\mathrm e}^{\textit {\_Z}}-4\right )-4 c_{1} +4 \textit {\_Z} -4 x +4\right )}}{4}-1-\frac {x^{2}}{4}+x \]
✓ Solution by Mathematica
Time used: 37.054 (sec). Leaf size: 248
DSolve[y'[x] == 1 - x/2 + x^2 - (3*x^3)/2 + (13*x^4)/16 - (3*x^5)/16 + x^6/64 - 2*x*y[x] + (7*x^2*y[x])/2 - (3*x^3*y[x])/2 + (3*x^4*y[x])/16 + y[x]^2 - 3*x*y[x]^2 + (3*x^2*y[x]^2)/4 + y[x]^3,y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [\frac {\sqrt [3]{2} \left (\frac {\frac {1}{4} \left (3 x^2-12 x+4\right )+3 y(x)}{\sqrt [3]{2}}+2^{2/3}\right ) \left (2^{2/3}-2^{2/3} \left (\frac {1}{4} \left (3 x^2-12 x+4\right )+3 y(x)\right )\right ) \left (\left (\frac {1}{4} \left (-3 x^2+12 x-4\right )-3 y(x)+1\right ) \log \left (2^{2/3}-2^{2/3} \left (\frac {1}{4} \left (3 x^2-12 x+4\right )+3 y(x)\right )\right )+\left (\frac {1}{4} \left (3 x^2-12 x+4\right )+3 y(x)-1\right ) \log \left (2 \left (\frac {\frac {1}{4} \left (3 x^2-12 x+4\right )+3 y(x)}{\sqrt [3]{2}}+2^{2/3}\right )\right )-3\right )}{9 \left (-\left (\frac {1}{4} \left (3 x^2-12 x+4\right )+3 y(x)\right )^3+3 \left (\frac {1}{4} \left (3 x^2-12 x+4\right )+3 y(x)\right )-2\right )}=\frac {1}{9} 2^{2/3} x+c_1,y(x)\right ] \]