68.8.39 problem 40 (b)

Internal problem ID [17462]
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 : 40 (b)
Date solved : Thursday, October 02, 2025 at 02:24:16 PM
CAS classification : [_separable]

\begin{align*} y^{\prime }&=\frac {t}{y^{3}} \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=0 \\ \end{align*}

✓ Maple. Time used: 0.067 (sec). Leaf size: 44

ode:=diff(y(t),t) = t/y(t)^3; 
ic:=[y(0) = 0]; 
dsolve([ode,op(ic)],y(t), singsol=all);
 

\begin{align*} y &= 2^{{1}/{4}} \sqrt {t} \\ y &= -2^{{1}/{4}} \sqrt {t} \\ y &= -i 2^{{1}/{4}} \sqrt {t} \\ y &= i 2^{{1}/{4}} \sqrt {t} \\ \end{align*}

✓ Mathematica. Time used: 0.136 (sec). Leaf size: 76

ode=D[y[t],t]==t/y[t]^3; 
ic={y[0]==0}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\begin{align*} y(t)&\to -\sqrt [4]{2} \sqrt [4]{t^2}\\ y(t)&\to -i \sqrt [4]{2} \sqrt [4]{t^2}\\ y(t)&\to i \sqrt [4]{2} \sqrt [4]{t^2}\\ y(t)&\to \sqrt [4]{2} \sqrt [4]{t^2} \end{align*}

✓ Sympy. Time used: 0.455 (sec). Leaf size: 61

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(-t/y(t)**3 + Derivative(y(t), t),0) 
ics = {y(0): 0} 
dsolve(ode,func=y(t),ics=ics)
 

\[ \left [ y{\left (t \right )} = - \sqrt [4]{2} i \sqrt [4]{t^{2}}, \ y{\left (t \right )} = \sqrt [4]{2} i \sqrt [4]{t^{2}}, \ y{\left (t \right )} = - \sqrt [4]{2} \sqrt [4]{t^{2}}, \ y{\left (t \right )} = \sqrt [4]{2} \sqrt [4]{t^{2}}\right ] \]