Internal problem ID [1669]
Book: Differential equations and their applications, 3rd ed., M. Braun
Section: Section 1.4. Page 24
Problem number: 2.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
Solve \begin {gather*} \boxed {y^{\prime }-\left (t +1\right ) \left (1+y\right )=0} \end {gather*}
✓ Solution by Maple
Time used: 0.003 (sec). Leaf size: 15
dsolve(diff(y(t),t) = (1+t)*(1+y(t)),y(t), singsol=all)
\[ y \relax (t ) = -1+{\mathrm e}^{\frac {t \left (2+t \right )}{2}} c_{1} \]
✓ Solution by Mathematica
Time used: 0.055 (sec). Leaf size: 25
DSolve[y'[t] == (1+t)*(1+y[t]),y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to -1+c_1 e^{\frac {1}{2} t (t+2)} \\ y(t)\to -1 \\ \end{align*}