Internal problem ID [6323]
Book: Own collection of miscellaneous problems
Section: section 1.0
Problem number: 33.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_quadrature]
Solve \begin {gather*} \boxed {y^{\prime }-\frac {1}{1-y}=0} \end {gather*} With initial conditions \begin {align*} [y \relax (0) = 2] \end {align*}
✓ Solution by Maple
Time used: 0.019 (sec). Leaf size: 13
dsolve([diff(y(t),t)=1/(1-y(t)),y(0) = 2],y(t), singsol=all)
\[ y \relax (t ) = 1+\sqrt {-2 t +1} \]
✓ Solution by Mathematica
Time used: 0.003 (sec). Leaf size: 16
DSolve[{y'[t]==1/(1-y[t]),y[0]==2},y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to \sqrt {1-2 t}+1 \\ \end{align*}