Internal problem ID [11392]
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.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_quadrature]
\[ \boxed {y^{\prime }-\frac {1}{2 y+1}=0} \] With initial conditions \begin {align*} [y \left (0\right ) = 1] \end {align*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 15
dsolve([diff(y(t),t)=1/(2*y(t)+1),y(0) = 1],y(t), singsol=all)
\[ y \left (t \right ) = -\frac {1}{2}+\frac {\sqrt {4 t +9}}{2} \]
✓ Solution by Mathematica
Time used: 0.004 (sec). Leaf size: 20
DSolve[{y'[t]==1/(2*y[t]+1),{y[0]==1}},y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to \frac {1}{2} \left (\sqrt {4 t+9}-1\right ) \]