72.8.23 problem 36

Internal problem ID [14787]
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 : 36
Date solved : Tuesday, January 28, 2025 at 07:15:26 AM
CAS classification : [_separable]

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

With initial conditions

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

✓ Solution by Maple

Time used: 0.086 (sec). Leaf size: 5

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

\[ y = t \]

✓ Solution by Mathematica

Time used: 0.500 (sec). Leaf size: 16

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

\[ y(t)\to \sqrt [3]{(t+1)^3}-1 \]