Internal problem ID [13408]
Book: Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell.
second edition. CRC Press. FL, USA. 2020
Section: Chapter 7. The exact form and general integrating fators. Additional exercises. page
141
Problem number: 7.4 (c).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
\[ \boxed {3 y^{\prime } y^{2}=2 x -2} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 60
dsolve(2-2*x+3*y(x)^2*diff(y(x),x)=0,y(x), singsol=all)
\begin{align*} y \left (x \right ) &= \left (x^{2}+c_{1} -2 x \right )^{\frac {1}{3}} \\ y \left (x \right ) &= -\frac {\left (x^{2}+c_{1} -2 x \right )^{\frac {1}{3}} \left (1+i \sqrt {3}\right )}{2} \\ y \left (x \right ) &= \frac {\left (x^{2}+c_{1} -2 x \right )^{\frac {1}{3}} \left (i \sqrt {3}-1\right )}{2} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.179 (sec). Leaf size: 71
DSolve[2-2*x+3*y[x]^2*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \sqrt [3]{x^2-2 x+3 c_1} \\ y(x)\to -\sqrt [3]{-1} \sqrt [3]{x^2-2 x+3 c_1} \\ y(x)\to (-1)^{2/3} \sqrt [3]{x^2-2 x+3 c_1} \\ \end{align*}