7.3.9 problem 9

Internal problem ID [2326]
Book : Differential equations and their applications, 3rd ed., M. Braun
Section : Section 1.4. Page 24
Problem number : 9
Date solved : Tuesday, September 30, 2025 at 05:26:51 AM
CAS classification : [_separable]

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

With initial conditions

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

✓ Maple. Time used: 0.090 (sec). Leaf size: 19

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

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

✓ Mathematica. Time used: 0.089 (sec). Leaf size: 26

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

\begin{align*} y(t)&\to 1-\sqrt {t^3+2 t^2+2 t+4} \end{align*}

✓ Sympy. Time used: 0.316 (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)
 

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