68.6.45 problem 51

Internal problem ID [17355]
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 : 51
Date solved : Thursday, October 02, 2025 at 02:10:17 PM
CAS classification : [[_homogeneous, `class A`], _rational, _Bernoulli]

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

✓ Maple. Time used: 0.002 (sec). Leaf size: 15

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

\[ y = \frac {t^{2}}{-t +c_1} \]

✓ Mathematica. Time used: 0.092 (sec). Leaf size: 23

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

\begin{align*} y(t)&\to -\frac {t^2}{t-c_1}\\ y(t)&\to 0 \end{align*}

✓ Sympy. Time used: 0.119 (sec). Leaf size: 8

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

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