72.8.25 problem 38

Internal problem ID [14789]
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. Review Exercises for chapter 1. page 136
Problem number : 38
Date solved : Tuesday, January 28, 2025 at 07:15:33 AM
CAS classification : [_quadrature]

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

With initial conditions

\begin{align*} y \left (0\right )&=1 \end{align*}

✓ Solution by Maple

Time used: 0.000 (sec). Leaf size: 5

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

\[ y = 1 \]

✓ Solution by Mathematica

Time used: 0.001 (sec). Leaf size: 6

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

\[ y(t)\to 1 \]