68.6.48 problem 54

Internal problem ID [17358]
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 : 54
Date solved : Thursday, October 02, 2025 at 02:10:23 PM
CAS classification : [[_homogeneous, `class D`], _rational, _Bernoulli]

\begin{align*} 5 t y^{2}+y+\left (2 t^{3}-t \right ) y^{\prime }&=0 \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 23

ode:=5*t*y(t)^2+y(t)+(2*t^3-t)*diff(y(t),t) = 0; 
dsolve(ode,y(t), singsol=all);
 

\[ y = \frac {2 t}{-5+2 \sqrt {2 t^{2}-1}\, c_1} \]

✓ Mathematica. Time used: 0.3 (sec). Leaf size: 78

ode=(5*t*y[t]^2+y[t])+(2*t^3-t)*D[y[t],t]==0; 
ic={}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\begin{align*} y(t)&\to \frac {\exp \left (\int _1^t\frac {1}{K[1]-2 K[1]^3}dK[1]\right )}{-\int _1^t\frac {5 \exp \left (\int _1^{K[2]}\frac {1}{K[1]-2 K[1]^3}dK[1]\right )}{1-2 K[2]^2}dK[2]+c_1}\\ y(t)&\to 0 \end{align*}

✓ Sympy. Time used: 0.240 (sec). Leaf size: 19

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(5*t*y(t)**2 + (2*t**3 - t)*Derivative(y(t), t) + y(t),0) 
ics = {} 
dsolve(ode,func=y(t),ics=ics)
 

\[ y{\left (t \right )} = \frac {2 t}{C_{1} \sqrt {2 t^{2} - 1} - 5} \]