Internal problem ID [2543]
Book: Advanced Mathematica, Book2, Perkin and Perkin, 1992
Section: Chapter 11.3, page 316
Problem number: 1.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
Solve \begin {gather*} \boxed {3 y^{2} y^{\prime }-2 x +1=0} \end {gather*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 78
dsolve(3*y(x)^2*diff(y(x),x)=2*x-1,y(x), singsol=all)
\begin{align*} y \relax (x ) = \left (x^{2}-x +c_{1}\right )^{\frac {1}{3}} \\ y \relax (x ) = -\frac {\left (x^{2}-x +c_{1}\right )^{\frac {1}{3}}}{2}-\frac {i \sqrt {3}\, \left (x^{2}-x +c_{1}\right )^{\frac {1}{3}}}{2} \\ y \relax (x ) = -\frac {\left (x^{2}-x +c_{1}\right )^{\frac {1}{3}}}{2}+\frac {i \sqrt {3}\, \left (x^{2}-x +c_{1}\right )^{\frac {1}{3}}}{2} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.242 (sec). Leaf size: 68
DSolve[3*y[x]^2*y'[x]==2*x-1,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \sqrt [3]{(x-1) x+3 c_1} \\ y(x)\to -\sqrt [3]{-1} \sqrt [3]{(x-1) x+3 c_1} \\ y(x)\to (-1)^{2/3} \sqrt [3]{(x-1) x+3 c_1} \\ \end{align*}