14.2.9 problem 9

Internal problem ID [2497]
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 : 9
Date solved : Sunday, March 30, 2025 at 12:03:35 AM
CAS classification : [_separable]

\begin{align*} y^{\prime }&=\frac {3 t^{2}+4 t +2}{2 y-2} \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=-1 \end{align*}

✓ Maple. Time used: 0.091 (sec). Leaf size: 19

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

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

✓ Mathematica. Time used: 0.158 (sec). Leaf size: 26

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

\[ y(t)\to 1-\sqrt {t^3+2 t^2+2 t+4} \]

✓ Sympy. Time used: 0.461 (sec). Leaf size: 20

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

\[ y{\left (t \right )} = 1 - \sqrt {t^{3} + 2 t^{2} + 2 t + 4} \]