Internal problem ID [3052]
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]
\[ \boxed {3 y^{2} y^{\prime }=2 x -1} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 60
dsolve(3*y(x)^2*diff(y(x),x)=2*x-1,y(x), singsol=all)
\begin{align*} y \left (x \right ) &= \left (x^{2}+c_{1} -x \right )^{\frac {1}{3}} \\ y \left (x \right ) &= -\frac {\left (x^{2}+c_{1} -x \right )^{\frac {1}{3}} \left (1+i \sqrt {3}\right )}{2} \\ y \left (x \right ) &= \frac {\left (x^{2}+c_{1} -x \right )^{\frac {1}{3}} \left (i \sqrt {3}-1\right )}{2} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.257 (sec). Leaf size: 71
DSolve[3*y[x]^2*y'[x]==2*x-1,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \sqrt [3]{x^2-x+3 c_1} \\ y(x)\to -\sqrt [3]{-1} \sqrt [3]{x^2-x+3 c_1} \\ y(x)\to (-1)^{2/3} \sqrt [3]{x^2-x+3 c_1} \\ \end{align*}