Internal problem ID [1993]
Book: Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath.
Boston. 1964
Section: Exercise 10, page 41
Problem number: 7.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class A`], _rational, [_Abel, `2nd type`, `class A`]]
\[ \boxed {y+\left (-3 y+2 x \right ) y^{\prime }=0} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 309
dsolve(y(x)+(2*x-3*y(x))*diff(y(x),x)=0,y(x), singsol=all)
\begin{align*} y \left (x \right ) &= \frac {\left (-108 c_{1} +8 x^{3}+12 \sqrt {3}\, \sqrt {c_{1} \left (-4 x^{3}+27 c_{1} \right )}\right )^{\frac {1}{3}}}{6}+\frac {2 x^{2}}{3 \left (-108 c_{1} +8 x^{3}+12 \sqrt {3}\, \sqrt {c_{1} \left (-4 x^{3}+27 c_{1} \right )}\right )^{\frac {1}{3}}}+\frac {x}{3} \\ y \left (x \right ) &= \frac {\left (-1-i \sqrt {3}\right ) \left (-108 c_{1} +8 x^{3}+12 \sqrt {3}\, \sqrt {-4 c_{1} x^{3}+27 c_{1}^{2}}\right )^{\frac {1}{3}}}{12}+\frac {\left (i \sqrt {3}\, x -x +\left (-108 c_{1} +8 x^{3}+12 \sqrt {3}\, \sqrt {-4 c_{1} x^{3}+27 c_{1}^{2}}\right )^{\frac {1}{3}}\right ) x}{3 \left (-108 c_{1} +8 x^{3}+12 \sqrt {3}\, \sqrt {-4 c_{1} x^{3}+27 c_{1}^{2}}\right )^{\frac {1}{3}}} \\ y \left (x \right ) &= \frac {\left (i \sqrt {3}-1\right ) \left (-108 c_{1} +8 x^{3}+12 \sqrt {3}\, \sqrt {-4 c_{1} x^{3}+27 c_{1}^{2}}\right )^{\frac {1}{3}}}{12}-\frac {\left (i \sqrt {3}\, x +x -\left (-108 c_{1} +8 x^{3}+12 \sqrt {3}\, \sqrt {-4 c_{1} x^{3}+27 c_{1}^{2}}\right )^{\frac {1}{3}}\right ) x}{3 \left (-108 c_{1} +8 x^{3}+12 \sqrt {3}\, \sqrt {-4 c_{1} x^{3}+27 c_{1}^{2}}\right )^{\frac {1}{3}}} \\ \end{align*}
✓ Solution by Mathematica
Time used: 60.066 (sec). Leaf size: 379
DSolve[y[x]+(2*x-3*y[x])*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{3} \left (\sqrt [3]{x^3+\frac {3}{2} \sqrt {3} \sqrt {e^{c_1} \left (-4 x^3+27 e^{c_1}\right )}-\frac {27 e^{c_1}}{2}}+\frac {x^2}{\sqrt [3]{x^3+\frac {3}{2} \sqrt {3} \sqrt {e^{c_1} \left (-4 x^3+27 e^{c_1}\right )}-\frac {27 e^{c_1}}{2}}}+x\right ) \\ y(x)\to \frac {1}{12} \left (i 2^{2/3} \left (\sqrt {3}+i\right ) \sqrt [3]{2 x^3+3 \sqrt {3} \sqrt {e^{c_1} \left (-4 x^3+27 e^{c_1}\right )}-27 e^{c_1}}-\frac {2 \left (1+i \sqrt {3}\right ) x^2}{\sqrt [3]{x^3+\frac {3}{2} \sqrt {3} \sqrt {e^{c_1} \left (-4 x^3+27 e^{c_1}\right )}-\frac {27 e^{c_1}}{2}}}+4 x\right ) \\ y(x)\to \frac {1}{12} \left (-2^{2/3} \left (1+i \sqrt {3}\right ) \sqrt [3]{2 x^3+3 \sqrt {3} \sqrt {e^{c_1} \left (-4 x^3+27 e^{c_1}\right )}-27 e^{c_1}}+\frac {2 i \left (\sqrt {3}+i\right ) x^2}{\sqrt [3]{x^3+\frac {3}{2} \sqrt {3} \sqrt {e^{c_1} \left (-4 x^3+27 e^{c_1}\right )}-\frac {27 e^{c_1}}{2}}}+4 x\right ) \\ \end{align*}