72.8.23 problem 36

Internal problem ID [14708]
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. Review Exercises for chapter 1. page 136
Problem number : 36
Date solved : Thursday, March 13, 2025 at 04:15:51 AM
CAS classification : [_separable]

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

With initial conditions

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

✓ Maple. Time used: 0.086 (sec). Leaf size: 5

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

\[ y = t \]

✓ Mathematica. Time used: 0.5 (sec). Leaf size: 16

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

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

✓ Sympy. Time used: 1.507 (sec). Leaf size: 20

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

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