73.6.5 problem 7.4 (c)

Internal problem ID [15144]
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)
Date solved : Tuesday, January 28, 2025 at 07:36:45 AM
CAS classification : [_separable]

\begin{align*} 2-2 x +3 y^{2} y^{\prime }&=0 \end{align*}

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 58

dsolve(2-2*x+3*y(x)^2*diff(y(x),x)=0,y(x), singsol=all)
 

\begin{align*} y &= \left (x^{2}+c_{1} -2 x \right )^{{1}/{3}} \\ y &= -\frac {\left (x^{2}+c_{1} -2 x \right )^{{1}/{3}} \left (1+i \sqrt {3}\right )}{2} \\ y &= \frac {\left (x^{2}+c_{1} -2 x \right )^{{1}/{3}} \left (i \sqrt {3}-1\right )}{2} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.187 (sec). Leaf size: 71

DSolve[2-2*x+3*y[x]^2*D[y[x],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*}