72.1.17 problem 20

Internal problem ID [14617]
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 : 20
Date solved : Tuesday, January 28, 2025 at 06:44:42 AM
CAS classification : [_separable]

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

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 39

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

\begin{align*} y &= -1-\sqrt {1+2 \ln \left (t +1\right )+2 c_{1}} \\ y &= -1+\sqrt {1+2 \ln \left (t +1\right )+2 c_{1}} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.125 (sec). Leaf size: 47

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

\begin{align*} y(t)\to -1-\sqrt {2 \log (t+1)+1+2 c_1} \\ y(t)\to -1+\sqrt {2 \log (t+1)+1+2 c_1} \\ \end{align*}