68.6.54 problem 59 (iii)

Internal problem ID [17364]
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 (iii)
Date solved : Thursday, October 02, 2025 at 02:11:59 PM
CAS classification : [[_homogeneous, `class A`], _exact, _rational, [_Abel, `2nd type`, `class A`]]

\begin{align*} 2 t +\frac {19 y}{10}+\left (\frac {19 t}{10}+2 y\right ) y^{\prime }&=0 \end{align*}

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

ode:=2*t+19/10*y(t)+(19/10*t+2*y(t))*diff(y(t),t) = 0; 
dsolve(ode,y(t), singsol=all);
 

\begin{align*} y &= \frac {-19 t c_1 -\sqrt {-39 t^{2} c_1^{2}+40}}{20 c_1} \\ y &= \frac {-19 t c_1 +\sqrt {-39 t^{2} c_1^{2}+40}}{20 c_1} \\ \end{align*}

✓ Mathematica. Time used: 0.246 (sec). Leaf size: 114

ode=(2*t+19/10*y[t])+(19/10*t+2*y[t])*D[y[t],t]==0; 
ic={}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\begin{align*} y(t)&\to \frac {1}{20} \left (-19 t-\sqrt {-39 t^2+40 e^{c_1}}\right )\\ y(t)&\to \frac {1}{20} \left (-19 t+\sqrt {-39 t^2+40 e^{c_1}}\right )\\ y(t)&\to \frac {1}{20} \left (-\sqrt {39} \sqrt {-t^2}-19 t\right )\\ y(t)&\to \frac {1}{20} \left (\sqrt {39} \sqrt {-t^2}-19 t\right ) \end{align*}

✓ Sympy. Time used: 0.893 (sec). Leaf size: 36

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(2*t + (19*t/10 + 2*y(t))*Derivative(y(t), t) + 19*y(t)/10,0) 
ics = {} 
dsolve(ode,func=y(t),ics=ics)
 

\[ \left [ y{\left (t \right )} = \frac {t \left (\sqrt {\frac {C_{1}}{t^{2}} - 39} - 19\right )}{20}, \ y{\left (t \right )} = \frac {t \left (- \sqrt {\frac {C_{1}}{t^{2}} - 39} - 19\right )}{20}\right ] \]