72.4.8 problem 15

Internal problem ID [14606]
Book : DIFFERENTIAL EQUATIONS by Paul Blanchard, Robert L. Devaney, Glen R. Hall. 4th edition. Brooks/Cole. Boston, USA. 2012
Section : Chapter 1. First-Order Differential Equations. Exercises section 1.5 page 71
Problem number : 15
Date solved : Thursday, March 13, 2025 at 04:08:39 AM
CAS classification : [_quadrature]

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

With initial conditions

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

✓ Maple. Time used: 0.038 (sec). Leaf size: 13

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

\[ y = \left (3 t +27\right )^{{1}/{3}}-2 \]

✓ Mathematica. Time used: 0.012 (sec). Leaf size: 20

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

\[ y(t)\to \sqrt [3]{3} \sqrt [3]{t+9}-2 \]

✓ Sympy. Time used: 1.274 (sec). Leaf size: 12

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

\[ y{\left (t \right )} = \sqrt [3]{3 t + 27} - 2 \]