74.8.13 problem 13

Internal problem ID [16078]
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 : 13
Date solved : Monday, March 31, 2025 at 02:39:04 PM
CAS classification : [[_homogeneous, `class A`], _rational, [_Abel, `2nd type`, `class B`]]

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

✓ Maple. Time used: 0.025 (sec). Leaf size: 45

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

\begin{align*} y &= \frac {1+\sqrt {t^{2} c_1 +1}}{c_1 t} \\ y &= \frac {1-\sqrt {t^{2} c_1 +1}}{c_1 t} \\ \end{align*}

✓ Mathematica. Time used: 0.118 (sec). Leaf size: 40

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

\[ \text {Solve}\left [\int _1^{\frac {y(t)}{t}}\frac {K[1]+1}{K[1] (2 K[1]+1)}dK[1]=-\log (t)+c_1,y(t)\right ] \]

✓ Sympy. Time used: 1.792 (sec). Leaf size: 31

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

\[ \left [ y{\left (t \right )} = \frac {C_{1} - \sqrt {C_{1} \left (C_{1} + t^{2}\right )}}{t}, \ y{\left (t \right )} = \frac {C_{1} + \sqrt {C_{1} \left (C_{1} + t^{2}\right )}}{t}\right ] \]