68.7.27 problem 27

Internal problem ID [17391]
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 : 27
Date solved : Thursday, October 02, 2025 at 02:16:18 PM
CAS classification : [[_homogeneous, `class A`], _rational, [_Abel, `2nd type`, `class B`]]

\begin{align*} y^{2}&=\left (y t -4 t^{2}\right ) y^{\prime } \end{align*}

✓ Maple. Time used: 0.009 (sec). Leaf size: 17

ode:=y(t)^2 = (t*y(t)-4*t^2)*diff(y(t),t); 
dsolve(ode,y(t), singsol=all);
 

\[ y = -4 t \operatorname {LambertW}\left (-\frac {{\mathrm e}^{-c_1}}{4 t}\right ) \]

✓ Mathematica. Time used: 2.22 (sec). Leaf size: 29

ode=y[t]^2==(t*y[t]-4*t^2)*D[y[t],t]; 
ic={}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\begin{align*} y(t)&\to -4 t W\left (-\frac {e^{-\frac {c_1}{4}}}{4 t}\right )\\ y(t)&\to 0 \end{align*}

✓ Sympy. Time used: 0.430 (sec). Leaf size: 12

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq((4*t**2 - t*y(t))*Derivative(y(t), t) + y(t)**2,0) 
ics = {} 
dsolve(ode,func=y(t),ics=ics)
 

\[ y{\left (t \right )} = - 4 t W\left (\frac {C_{1}}{t}\right ) \]