74.4.2 problem 2

Internal problem ID [15895]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 2. First Order Equations. Exercises 2.2, page 39
Problem number : 2
Date solved : Tuesday, January 28, 2025 at 08:17:45 AM
CAS classification : [_separable]

\begin{align*} \frac {1}{2 \sqrt {t}}+y^{2} y^{\prime }&=0 \end{align*}

✓ Solution by Maple

Time used: 0.007 (sec). Leaf size: 55

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

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

✓ Solution by Mathematica

Time used: 1.782 (sec). Leaf size: 79

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

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