Internal problem ID [14205]
Book: INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton.
Fourth edition 2014. ElScAe. 2014
Section: Chapter 2. First Order Equations. Exercises 2.2, page 39
Problem number: 47.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
\[ \boxed {y^{\prime }-\frac {{\mathrm e}^{t}}{y+1}=0} \] With initial conditions \begin {align*} [y \left (0\right ) = -2] \end {align*}
✓ Solution by Maple
Time used: 0.093 (sec). Leaf size: 16
dsolve([diff(y(t),t)=exp(t)/(y(t)+1),y(0) = -2],y(t), singsol=all)
\[ y \left (t \right ) = -1-\sqrt {2 \,{\mathrm e}^{t}-1} \]
✓ Solution by Mathematica
Time used: 0.593 (sec). Leaf size: 20
DSolve[{y'[t]==Exp[t]/(y[t]+1),{y[0]==-2}},y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to -\sqrt {2 e^t-1}-1 \]