56.1.32 problem 33

Internal problem ID [8744]
Book : Own collection of miscellaneous problems
Section : section 1.0
Problem number : 33
Date solved : Monday, January 27, 2025 at 04:46:09 PM
CAS classification : [_quadrature]

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

With initial conditions

\begin{align*} y \left (0\right )&=2 \end{align*}

✓ Solution by Maple

Time used: 0.020 (sec). Leaf size: 13

dsolve([diff(y(t),t)=1/(1-y(t)),y(0) = 2],y(t), singsol=all)
 

\[ y = 1+\sqrt {-2 t +1} \]

✓ Solution by Mathematica

Time used: 0.003 (sec). Leaf size: 16

DSolve[{D[y[t],t]==1/(1-y[t]),y[0]==2},y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to \sqrt {1-2 t}+1 \]