Internal problem ID [12556]
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.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_quadrature]
\[ \boxed {y^{\prime }-\frac {1}{2 y+1}=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 35
dsolve(diff(y(t),t)=1/(2*y(t)+1),y(t), singsol=all)
\begin{align*} y \left (t \right ) = -\frac {1}{2}-\frac {\sqrt {1+4 t +4 c_{1}}}{2} y \left (t \right ) = -\frac {1}{2}+\frac {\sqrt {1+4 t +4 c_{1}}}{2} \end{align*}
✓ Solution by Mathematica
Time used: 0.14 (sec). Leaf size: 49
DSolve[y'[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*}