Internal problem ID [14300]
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.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_quadrature]
\[ \boxed {3 y^{2} y^{\prime }=1} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 45
dsolve(-1+3*y(t)^2*diff(y(t),t)=0,y(t), singsol=all)
\begin{align*} y \left (t \right ) &= \left (t +c_{1} \right )^{\frac {1}{3}} \\ y \left (t \right ) &= -\frac {\left (t +c_{1} \right )^{\frac {1}{3}} \left (1+i \sqrt {3}\right )}{2} \\ y \left (t \right ) &= \frac {\left (t +c_{1} \right )^{\frac {1}{3}} \left (i \sqrt {3}-1\right )}{2} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.036 (sec). Leaf size: 56
DSolve[-1+3*y[t]^2*y'[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*}