Internal problem ID [1919]
Book: Differential Equations, Nelson, Folley, Coral, 3rd ed, 1964
Section: Exercis 6, page 25
Problem number: 20.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class A], _rational, [_Abel, 2nd type, class B]]
Solve \begin {gather*} \boxed {\left (3 x y-2 x^{2}\right ) y^{\prime }-2 y^{2}+x y=0} \end {gather*} With initial conditions \begin {align*} [y \relax (1) = -1] \end {align*}
✓ Solution by Maple
Time used: 0.528 (sec). Leaf size: 116
dsolve([(3*x*y(x)-2*x^2)*diff(y(x),x)=2*y(x)^2-x*y(x),y(1) = -1],y(x), singsol=all)
\[ y \relax (x ) = \frac {\left (i \sqrt {3}-1\right ) \left (-27 x^{2}+x^{3}+3 \sqrt {3}\, \sqrt {-2 x^{5}+27 x^{4}}\right )^{\frac {1}{3}}}{6}-\frac {x \left (i \sqrt {3}\, x +x -2 \left (-27 x^{2}+x^{3}+3 \sqrt {3}\, \sqrt {-2 x^{5}+27 x^{4}}\right )^{\frac {1}{3}}\right )}{6 \left (-27 x^{2}+x^{3}+3 \sqrt {3}\, \sqrt {-2 x^{5}+27 x^{4}}\right )^{\frac {1}{3}}} \]
✓ Solution by Mathematica
Time used: 14.166 (sec). Leaf size: 134
DSolve[{(3*x*y[x]-2*x^2)*y'[x]==2*y[x]^2-x*y[x],y[1]==-1},y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {\left (\sqrt [3]{3 \sqrt {3} \sqrt {(27-2 x) x^4}+(x-27) x^2}-x\right ) \left (i \left (\sqrt {3}+i\right ) \sqrt [3]{3 \sqrt {3} \sqrt {(27-2 x) x^4}+(x-27) x^2}+i \sqrt {3} x+x\right )}{6 \sqrt [3]{3 \sqrt {3} \sqrt {(27-2 x) x^4}+(x-27) x^2}} \\ \end{align*}