25.1.1 problem 1

Internal problem ID [4213]
Book : Advanced Mathematica, Book2, Perkin and Perkin, 1992
Section : Chapter 11.3, page 316
Problem number : 1
Date solved : Monday, January 27, 2025 at 08:42:31 AM
CAS classification : [_separable]

\begin{align*} 3 y^{2} y^{\prime }&=2 x -1 \end{align*}

✓ Solution by Maple

Time used: 0.006 (sec). Leaf size: 58

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

✓ Solution by Mathematica

Time used: 0.232 (sec). Leaf size: 71

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