63.4.15 problem 5

Internal problem ID [13058]
Book : A First Course in Differential Equations by J. David Logan. Third Edition. Springer-Verlag, NY. 2015.
Section : Chapter 1, First order differential equations. Section 1.3.1 Separable equations. Exercises page 26
Problem number : 5
Date solved : Tuesday, January 28, 2025 at 04:50:41 AM
CAS classification : [_quadrature]

\begin{align*} y^{\prime }&=\frac {1}{2 y+1} \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)+1),y(0) = 1],y(t), singsol=all)
 

\[ y = -\frac {1}{2}+\frac {\sqrt {9+4 t}}{2} \]

✓ Solution by Mathematica

Time used: 0.005 (sec). Leaf size: 20

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

\[ y(t)\to \frac {1}{2} \left (\sqrt {4 t+9}-1\right ) \]