74.8.1 problem 1

Internal problem ID [16137]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 2. First Order Equations. Review exercises, page 80
Problem number : 1
Date solved : Tuesday, January 28, 2025 at 08:51:39 AM
CAS classification : [_separable]

\begin{align*} y^{\prime }&=\frac {2 t^{5}}{5 y^{2}} \end{align*}

✓ Solution by Maple

Time used: 0.005 (sec). Leaf size: 63

dsolve(diff(y(t),t)=2*t^5/(5*y(t)^2),y(t), singsol=all)
 

\begin{align*} y &= \frac {\left (25 t^{6}+125 c_{1} \right )^{{1}/{3}}}{5} \\ y &= -\frac {\left (25 t^{6}+125 c_{1} \right )^{{1}/{3}} \left (1+i \sqrt {3}\right )}{10} \\ y &= \frac {\left (25 t^{6}+125 c_{1} \right )^{{1}/{3}} \left (i \sqrt {3}-1\right )}{10} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.206 (sec). Leaf size: 72

DSolve[D[y[t],t]==2*t^5/(5*y[t]^2),y[t],t,IncludeSingularSolutions -> True]
 

\begin{align*} y(t)\to -\sqrt [3]{-\frac {1}{5}} \sqrt [3]{t^6+15 c_1} \\ y(t)\to \sqrt [3]{\frac {t^6}{5}+3 c_1} \\ y(t)\to (-1)^{2/3} \sqrt [3]{\frac {t^6}{5}+3 c_1} \\ \end{align*}