74.7.7 problem 7

Internal problem ID [16005]
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 : 7
Date solved : Thursday, March 13, 2025 at 07:12:19 AM
CAS classification : [[_homogeneous, `class D`], _rational, _Bernoulli]

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

✓ Maple. Time used: 0.003 (sec). Leaf size: 16

ode:=diff(y(t),t)-y(t)/t = t*y(t)^2; 
dsolve(ode,y(t), singsol=all);
 

\[ y = -\frac {3 t}{t^{3}-3 c_{1}} \]

✓ Mathematica. Time used: 0.135 (sec). Leaf size: 23

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

\begin{align*} y(t)\to -\frac {3 t}{t^3-3 c_1} \\ y(t)\to 0 \\ \end{align*}

✓ Sympy. Time used: 0.176 (sec). Leaf size: 10

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

\[ y{\left (t \right )} = \frac {3 t}{C_{1} - t^{3}} \]