72.1.1 problem 1

Internal problem ID [14601]
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 : 1
Date solved : Tuesday, January 28, 2025 at 06:44:08 AM
CAS classification : [_separable]

\begin{align*} y^{\prime }&=\frac {y+1}{1+t} \end{align*}

✓ Solution by Maple

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

dsolve(diff(y(t),t)=(y(t)+1)/(t+1),y(t), singsol=all)
 

\[ y = c_{1} t +c_{1} -1 \]

✓ Solution by Mathematica

Time used: 0.025 (sec). Leaf size: 18

DSolve[D[y[t],t]==(y[t]+1)/(t+1),y[t],t,IncludeSingularSolutions -> True]
 

\begin{align*} y(t)\to -1+c_1 (t+1) \\ y(t)\to -1 \\ \end{align*}