68.6.12 problem 13

Internal problem ID [17322]
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 : 13
Date solved : Thursday, October 02, 2025 at 02:02:31 PM
CAS classification : [_separable]

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

✓ Maple. Time used: 0.004 (sec). Leaf size: 32

ode:=y(t)^2+2*t*y(t)*diff(y(t),t) = 0; 
dsolve(ode,y(t), singsol=all);
 

\begin{align*} y &= 0 \\ y &= \frac {\sqrt {-t c_1}}{t} \\ y &= -\frac {\sqrt {-t c_1}}{t} \\ \end{align*}

✓ Mathematica. Time used: 0.015 (sec). Leaf size: 23

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

\begin{align*} y(t)&\to 0\\ y(t)&\to \frac {c_1}{\sqrt {t}}\\ y(t)&\to 0 \end{align*}

✓ Sympy. Time used: 0.104 (sec). Leaf size: 8

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

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