72.1.12 problem 15

Internal problem ID [14612]
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 : 15
Date solved : Tuesday, January 28, 2025 at 06:44:32 AM
CAS classification : [_quadrature]

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

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 35

dsolve(diff(y(t),t)=1/(2*y(t)+1),y(t), singsol=all)
 

\begin{align*} y &= -\frac {1}{2}-\frac {\sqrt {1+4 c_{1} +4 t}}{2} \\ y &= -\frac {1}{2}+\frac {\sqrt {1+4 c_{1} +4 t}}{2} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.085 (sec). Leaf size: 49

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

\begin{align*} y(t)\to \frac {1}{2} \left (-1-\sqrt {4 t+1+4 c_1}\right ) \\ y(t)\to \frac {1}{2} \left (-1+\sqrt {4 t+1+4 c_1}\right ) \\ \end{align*}