72.1.33 problem 36

Internal problem ID [14554]
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 1.2. page 33
Problem number : 36
Date solved : Thursday, March 13, 2025 at 03:33:57 AM
CAS classification : [_quadrature]

\begin{align*} y^{\prime }&=\frac {1}{2 y+3} \end{align*}

With initial conditions

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

✓ Maple. Time used: 0.027 (sec). Leaf size: 15

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

\[ y = -\frac {3}{2}+\frac {\sqrt {25+4 t}}{2} \]

✓ Mathematica. Time used: 0.003 (sec). Leaf size: 20

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

\[ y(t)\to \frac {1}{2} \left (\sqrt {4 t+25}-3\right ) \]

✓ Sympy. Time used: 0.311 (sec). Leaf size: 15

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

\[ y{\left (t \right )} = \frac {\sqrt {4 t + 25}}{2} - \frac {3}{2} \]