74.7.39 problem 39

Internal problem ID [16045]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 2. First Order Equations. Exercises 2.5, page 64
Problem number : 39
Date solved : Monday, March 31, 2025 at 02:34:49 PM
CAS classification : [[_homogeneous, `class A`], _rational, _Bernoulli]

\begin{align*} y^{3}-t^{3}-t y^{2} y^{\prime }&=0 \end{align*}

With initial conditions

\begin{align*} y \left (1\right )&=3 \end{align*}

✓ Maple. Time used: 0.102 (sec). Leaf size: 14

ode:=y(t)^3-t^3-t*y(t)^2*diff(y(t),t) = 0; 
ic:=y(1) = 3; 
dsolve([ode,ic],y(t), singsol=all);
 

\[ y = \left (-3 \ln \left (t \right )+27\right )^{{1}/{3}} t \]

✓ Mathematica. Time used: 0.195 (sec). Leaf size: 22

ode=(y[t]^3-t^3)-(t*y[t]^2)*D[y[t],t]==0; 
ic={y[1]==3}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\[ y(t)\to \sqrt [3]{3} t \sqrt [3]{9-\log (t)} \]

✓ Sympy. Time used: 1.467 (sec). Leaf size: 15

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(-t**3 - t*y(t)**2*Derivative(y(t), t) + y(t)**3,0) 
ics = {y(1): 3} 
dsolve(ode,func=y(t),ics=ics)
 

\[ y{\left (t \right )} = \sqrt [3]{t^{3} \left (27 - 3 \log {\left (t \right )}\right )} \]