72.1.24 problem 27

Internal problem ID [14624]
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 1.2. page 33
Problem number : 27
Date solved : Tuesday, January 28, 2025 at 06:44:56 AM
CAS classification : [_quadrature]

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

With initial conditions

\begin{align*} y \left (0\right )&={\frac {1}{2}} \end{align*}

✓ Solution by Maple

Time used: 0.027 (sec). Leaf size: 9

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

\[ y = \frac {1}{t +2} \]

✓ Solution by Mathematica

Time used: 0.003 (sec). Leaf size: 10

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

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