68.6.53 problem 59 (ii)

Internal problem ID [17363]
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 : 59 (ii)
Date solved : Thursday, October 02, 2025 at 02:11:55 PM
CAS classification : [[_homogeneous, `class A`], _exact, _rational, [_Abel, `2nd type`, `class A`]]

\begin{align*} \frac {9 t}{5}+2 y+\left (2 t +2 y\right ) y^{\prime }&=0 \end{align*}

✓ Maple. Time used: 0.012 (sec). Leaf size: 53

ode:=9/5*t+2*y(t)+(2*t+2*y(t))*diff(y(t),t) = 0; 
dsolve(ode,y(t), singsol=all);
 

\begin{align*} y &= \frac {-10 t c_1 -\sqrt {10 t^{2} c_1^{2}+10}}{10 c_1} \\ y &= \frac {-10 t c_1 +\sqrt {10 t^{2} c_1^{2}+10}}{10 c_1} \\ \end{align*}

✓ Mathematica. Time used: 0.3 (sec). Leaf size: 101

ode=(18/10*t+2*y[t])+(2*t+2*y[t])*D[y[t],t]==0; 
ic={}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\begin{align*} y(t)&\to -t-\frac {\sqrt {t^2+e^{20 c_1}}}{\sqrt {10}}\\ y(t)&\to -t+\frac {\sqrt {t^2+e^{20 c_1}}}{\sqrt {10}}\\ y(t)&\to -\frac {\sqrt {t^2}}{\sqrt {10}}-t\\ y(t)&\to \frac {\sqrt {t^2}}{\sqrt {10}}-t \end{align*}

✓ Sympy. Time used: 0.848 (sec). Leaf size: 32

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(9*t/5 + (2*t + 2*y(t))*Derivative(y(t), t) + 2*y(t),0) 
ics = {} 
dsolve(ode,func=y(t),ics=ics)
 

\[ \left [ y{\left (t \right )} = - t - \frac {\sqrt {C_{1} + 10 t^{2}}}{10}, \ y{\left (t \right )} = - t + \frac {\sqrt {C_{1} + 10 t^{2}}}{10}\right ] \]