Internal problem ID [12649]
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 1.6 page 89
Problem number: 6.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_quadrature]
\[ \boxed {y^{\prime }-\frac {1}{-2+y}=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 33
dsolve(diff(y(t),t)=1/(y(t)-2),y(t), singsol=all)
\begin{align*} y \left (t \right ) = 2-\sqrt {4+2 c_{1} +2 t} y \left (t \right ) = 2+\sqrt {4+2 c_{1} +2 t} \end{align*}
✓ Solution by Mathematica
Time used: 0.145 (sec). Leaf size: 44
DSolve[y'[t]==1/(y[t]-2),y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to 2-\sqrt {2} \sqrt {t+2+c_1} y(t)\to 2+\sqrt {2} \sqrt {t+2+c_1} \end{align*}