Internal problem ID [12881]
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.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
\[ \boxed {y^{\prime }-\frac {1}{1+t y+y+t}=0} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 39
dsolve(diff(y(t),t)=1/(t*y(t)+t+y(t)+1),y(t), singsol=all)
\begin{align*} y \left (t \right ) &= -1-\sqrt {1+2 \ln \left (t +1\right )+2 c_{1}} \\ y \left (t \right ) &= -1+\sqrt {1+2 \ln \left (t +1\right )+2 c_{1}} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.217 (sec). Leaf size: 47
DSolve[y'[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*}