72.8.32 problem 47

Internal problem ID [14796]
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 : 47
Date solved : Tuesday, January 28, 2025 at 07:15:51 AM
CAS classification : [_quadrature]

\begin{align*} y^{\prime }&=3-y^{2} \end{align*}

With initial conditions

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

✓ Solution by Maple

Time used: 0.072 (sec). Leaf size: 14

dsolve([diff(y(t),t)=3-y(t)^2,y(0) = 0],y(t), singsol=all)
 

\[ y = \sqrt {3}\, \tanh \left (\sqrt {3}\, t \right ) \]

✓ Solution by Mathematica

Time used: 0.025 (sec). Leaf size: 37

DSolve[{D[y[t],t]==3-y[t]^2,{y[0]==0}},y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to \frac {\sqrt {3} \left (e^{2 \sqrt {3} t}-1\right )}{e^{2 \sqrt {3} t}+1} \]