74.8.1 problem 1

Internal problem ID [16066]
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 : Monday, March 31, 2025 at 02:38:27 PM
CAS classification : [_separable]

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

✓ Maple. Time used: 0.003 (sec). Leaf size: 63

ode:=diff(y(t),t) = 2/5*t^5/y(t)^2; 
dsolve(ode,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 (-1+i \sqrt {3}\right )}{10} \\ \end{align*}

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

ode=D[y[t],t]==2*t^5/(5*y[t]^2); 
ic={}; 
DSolve[{ode,ic},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*}

✓ Sympy. Time used: 0.747 (sec). Leaf size: 58

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(-2*t**5/(5*y(t)**2) + Derivative(y(t), t),0) 
ics = {} 
dsolve(ode,func=y(t),ics=ics)
 

\[ \left [ y{\left (t \right )} = \sqrt [3]{C_{1} + \frac {t^{6}}{5}}, \ y{\left (t \right )} = \frac {\left (-1 - \sqrt {3} i\right ) \sqrt [3]{C_{1} + \frac {t^{6}}{5}}}{2}, \ y{\left (t \right )} = \frac {\left (-1 + \sqrt {3} i\right ) \sqrt [3]{C_{1} + \frac {t^{6}}{5}}}{2}\right ] \]