68.6.30 problem 31

Internal problem ID [17340]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 2. First Order Equations. Exercises 2.4, page 57
Problem number : 31
Date solved : Thursday, October 02, 2025 at 02:06:03 PM
CAS classification : [_separable]

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

With initial conditions

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

✓ Maple. Time used: 0.039 (sec). Leaf size: 7

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

\[ y = \frac {1}{t} \]

✓ Mathematica. Time used: 0.017 (sec). Leaf size: 8

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

\begin{align*} y(t)&\to \frac {1}{t} \end{align*}

✓ Sympy. Time used: 0.104 (sec). Leaf size: 5

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

\[ y{\left (t \right )} = \frac {1}{t} \]