72.4.8 problem 15

Internal problem ID [14685]
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 1.5 page 71
Problem number : 15
Date solved : Tuesday, January 28, 2025 at 07:11:18 AM
CAS classification : [_quadrature]

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

With initial conditions

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

✓ Solution by Maple

Time used: 0.038 (sec). Leaf size: 13

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

\[ y = \left (3 t +27\right )^{{1}/{3}}-2 \]

✓ Solution by Mathematica

Time used: 0.012 (sec). Leaf size: 20

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

\[ y(t)\to \sqrt [3]{3} \sqrt [3]{t+9}-2 \]