72.4.9 problem 16

Internal problem ID [14607]
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 : 16
Date solved : Thursday, March 13, 2025 at 04:08:42 AM
CAS classification : [_separable]

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

With initial conditions

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

✓ Maple. Time used: 0.036 (sec). Leaf size: 15

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

\[ y = 2-\sqrt {t^{2}+3} \]

✓ Mathematica. Time used: 0.003 (sec). Leaf size: 21

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

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

✓ Sympy. Time used: 0.282 (sec). Leaf size: 12

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

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