72.5.19 problem 6

Internal problem ID [14705]
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
Date solved : Tuesday, January 28, 2025 at 07:12:07 AM
CAS classification : [_quadrature]

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

✓ Solution by Maple

Time used: 0.005 (sec). Leaf size: 33

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

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

✓ Solution by Mathematica

Time used: 0.081 (sec). Leaf size: 44

DSolve[D[y[t],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*}