72.1.33 problem 36

Internal problem ID [14633]
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 : Tuesday, January 28, 2025 at 06:45:27 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*}

✓ Solution by Maple

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

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

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

✓ Solution by Mathematica

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

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

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