74.7.43 problem 42 (b)

Internal problem ID [16049]
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 : 42 (b)
Date solved : Monday, March 31, 2025 at 02:36:51 PM
CAS classification : [[_homogeneous, `class C`], _exact, _rational, [_Abel, `2nd type`, `class A`]]

\begin{align*} 5 t +2 y+1+\left (2 t +y+1\right ) y^{\prime }&=0 \end{align*}

✓ Maple. Time used: 0.188 (sec). Leaf size: 32

ode:=5*t+2*y(t)+1+(2*t+y(t)+1)*diff(y(t),t) = 0; 
dsolve(ode,y(t), singsol=all);
 

\[ y = \frac {-\sqrt {-\left (t -1\right )^{2} c_1^{2}+1}+\left (-2 t -1\right ) c_1}{c_1} \]

✓ Mathematica. Time used: 0.155 (sec). Leaf size: 53

ode=(5*t+2*y[t]+1)+(2*t+y[t]+1)*D[y[t],t]==0; 
ic={}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\begin{align*} y(t)\to -\sqrt {-t^2+2 t+1+c_1}-2 t-1 \\ y(t)\to \sqrt {-t^2+2 t+1+c_1}-2 t-1 \\ \end{align*}

✓ Sympy. Time used: 1.845 (sec). Leaf size: 39

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(5*t + (2*t + y(t) + 1)*Derivative(y(t), t) + 2*y(t) + 1,0) 
ics = {} 
dsolve(ode,func=y(t),ics=ics)
 

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