Internal problem ID [7827]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, linear first order
Problem number: 247.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class C], _rational, [_Abel, 2nd type, class B]]
Solve \begin {gather*} \boxed {\left (3 x +2\right ) \left (y-2 x -1\right ) y^{\prime }-y^{2}+y x -7 x^{2}-9 x -3=0} \end {gather*}
✓ Solution by Maple
Time used: 0.922 (sec). Leaf size: 517
dsolve((3*x+2)*(y(x)-2*x-1)*diff(y(x),x)-y(x)^2+x*y(x)-7*x^2-9*x-3=0,y(x), singsol=all)
\[ y \relax (x ) = -\frac {1}{3}+\frac {\left (3 x +2\right ) \left (7 \left (-\frac {\left (2 \left (3 x +2\right ) c_{1}-27 \left (3 x +2\right )^{3} c_{1}^{3}+2 \sqrt {-27 \left (3 x +2\right )^{4} c_{1}^{4}+\left (3 x +2\right )^{2} c_{1}^{2}}\right )^{\frac {1}{3}}}{4}-\frac {9 \left (3 x +2\right )^{2} c_{1}^{2}}{4 \left (2 \left (3 x +2\right ) c_{1}-27 \left (3 x +2\right )^{3} c_{1}^{3}+2 \sqrt {-27 \left (3 x +2\right )^{4} c_{1}^{4}+\left (3 x +2\right )^{2} c_{1}^{2}}\right )^{\frac {1}{3}}}-\frac {3 \left (3 x +2\right ) c_{1}}{2}+\frac {i \sqrt {3}\, \left (\frac {\left (2 \left (3 x +2\right ) c_{1}-27 \left (3 x +2\right )^{3} c_{1}^{3}+2 \sqrt {-27 \left (3 x +2\right )^{4} c_{1}^{4}+\left (3 x +2\right )^{2} c_{1}^{2}}\right )^{\frac {1}{3}}}{2}-\frac {9 \left (3 x +2\right )^{2} c_{1}^{2}}{2 \left (2 \left (3 x +2\right ) c_{1}-27 \left (3 x +2\right )^{3} c_{1}^{3}+2 \sqrt {-27 \left (3 x +2\right )^{4} c_{1}^{4}+\left (3 x +2\right )^{2} c_{1}^{2}}\right )^{\frac {1}{3}}}\right )}{2}\right )^{2}-1\right )}{6 \left (-\frac {\left (2 \left (3 x +2\right ) c_{1}-27 \left (3 x +2\right )^{3} c_{1}^{3}+2 \sqrt {-27 \left (3 x +2\right )^{4} c_{1}^{4}+\left (3 x +2\right )^{2} c_{1}^{2}}\right )^{\frac {1}{3}}}{4}-\frac {9 \left (3 x +2\right )^{2} c_{1}^{2}}{4 \left (2 \left (3 x +2\right ) c_{1}-27 \left (3 x +2\right )^{3} c_{1}^{3}+2 \sqrt {-27 \left (3 x +2\right )^{4} c_{1}^{4}+\left (3 x +2\right )^{2} c_{1}^{2}}\right )^{\frac {1}{3}}}-\frac {3 \left (3 x +2\right ) c_{1}}{2}+\frac {i \sqrt {3}\, \left (\frac {\left (2 \left (3 x +2\right ) c_{1}-27 \left (3 x +2\right )^{3} c_{1}^{3}+2 \sqrt {-27 \left (3 x +2\right )^{4} c_{1}^{4}+\left (3 x +2\right )^{2} c_{1}^{2}}\right )^{\frac {1}{3}}}{2}-\frac {9 \left (3 x +2\right )^{2} c_{1}^{2}}{2 \left (2 \left (3 x +2\right ) c_{1}-27 \left (3 x +2\right )^{3} c_{1}^{3}+2 \sqrt {-27 \left (3 x +2\right )^{4} c_{1}^{4}+\left (3 x +2\right )^{2} c_{1}^{2}}\right )^{\frac {1}{3}}}\right )}{2}\right )^{2}} \]
✓ Solution by Mathematica
Time used: 66.925 (sec). Leaf size: 486
DSolve[(3*x+2)*(y[x]-2*x-1)*y'[x]-y[x]^2+x*y[x]-7*x^2-9*x-3==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {x}{2}+\frac {(3 x+2)^2}{2 \sqrt [3]{(3 x+2)^3-2 e^{2 c_1} (3 x+2)+2 \sqrt {e^{4 c_1} (3 x+2)^2-e^{2 c_1} (3 x+2)^4}}}+\frac {1}{2} \sqrt [3]{(3 x+2)^3-2 e^{2 c_1} (3 x+2)+2 \sqrt {e^{4 c_1} (3 x+2)^2-e^{2 c_1} (3 x+2)^4}} \\ y(x)\to \frac {x}{2}-\frac {i \left (\sqrt {3}-i\right ) (3 x+2)^2}{4 \sqrt [3]{(3 x+2)^3-2 e^{2 c_1} (3 x+2)+2 \sqrt {e^{4 c_1} (3 x+2)^2-e^{2 c_1} (3 x+2)^4}}}+\frac {1}{4} i \left (\sqrt {3}+i\right ) \sqrt [3]{(3 x+2)^3-2 e^{2 c_1} (3 x+2)+2 \sqrt {e^{4 c_1} (3 x+2)^2-e^{2 c_1} (3 x+2)^4}} \\ y(x)\to \frac {x}{2}+\frac {i \left (\sqrt {3}+i\right ) (3 x+2)^2}{4 \sqrt [3]{(3 x+2)^3-2 e^{2 c_1} (3 x+2)+2 \sqrt {e^{4 c_1} (3 x+2)^2-e^{2 c_1} (3 x+2)^4}}}-\frac {1}{4} i \left (\sqrt {3}-i\right ) \sqrt [3]{(3 x+2)^3-2 e^{2 c_1} (3 x+2)+2 \sqrt {e^{4 c_1} (3 x+2)^2-e^{2 c_1} (3 x+2)^4}} \\ \end{align*}