14.2.21 problem 23

Internal problem ID [2509]
Book : Differential equations and their applications, 4th ed., M. Braun
Section : Chapter 1. First order differential equations. Section 1.4 separable equations. Excercises page 24
Problem number : 23
Date solved : Sunday, March 30, 2025 at 12:05:53 AM
CAS classification : [[_homogeneous, `class C`], _exact, _rational, [_Abel, `2nd type`, `class A`]]

\begin{align*} t +2 y+3+\left (2 t +4 y-1\right ) y^{\prime }&=0 \end{align*}

✓ Maple. Time used: 0.008 (sec). Leaf size: 41

ode:=t+2*y(t)+3+(2*t+4*y(t)-1)*diff(y(t),t) = 0; 
dsolve(ode,y(t), singsol=all);
 

\begin{align*} y &= -\frac {t}{2}+\frac {1}{4}-\frac {\sqrt {28 c_1 -28 t +1}}{4} \\ y &= -\frac {t}{2}+\frac {1}{4}+\frac {\sqrt {28 c_1 -28 t +1}}{4} \\ \end{align*}

✓ Mathematica. Time used: 0.128 (sec). Leaf size: 55

ode=(t+2*y[t]+3)+(2*t+4*y[t]-1)*D[y[t],t]==0; 
ic={}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\begin{align*} y(t)\to \frac {1}{4} \left (-2 t-\sqrt {-28 t+1+16 c_1}+1\right ) \\ y(t)\to \frac {1}{4} \left (-2 t+\sqrt {-28 t+1+16 c_1}+1\right ) \\ \end{align*}

✓ Sympy. Time used: 1.109 (sec). Leaf size: 37

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(t + (2*t + 4*y(t) - 1)*Derivative(y(t), t) + 2*y(t) + 3,0) 
ics = {} 
dsolve(ode,func=y(t),ics=ics)
 

\[ \left [ y{\left (t \right )} = - \frac {t}{2} - \frac {\sqrt {C_{1} - 28 t}}{4} + \frac {1}{4}, \ y{\left (t \right )} = - \frac {t}{2} + \frac {\sqrt {C_{1} - 28 t}}{4} + \frac {1}{4}\right ] \]