74.6.11 problem 12

Internal problem ID [16034]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 2. First Order Equations. Exercises 2.4, page 57
Problem number : 12
Date solved : Tuesday, January 28, 2025 at 08:28:21 AM
CAS classification : [_quadrature]

\begin{align*} -1+3 y^{2} y^{\prime }&=0 \end{align*}

✓ Solution by Maple

Time used: 0.005 (sec). Leaf size: 43

dsolve(-1+3*y(t)^2*diff(y(t),t)=0,y(t), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.038 (sec). Leaf size: 56

DSolve[-1+3*y[t]^2*D[y[t],t]==0,y[t],t,IncludeSingularSolutions -> True]
 

\begin{align*} y(t)\to \sqrt [3]{t+3 c_1} \\ y(t)\to -\sqrt [3]{-1} \sqrt [3]{t+3 c_1} \\ y(t)\to (-1)^{2/3} \sqrt [3]{t+3 c_1} \\ \end{align*}