Internal problem ID [14261]
Book: INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton.
Fourth edition 2014. ElScAe. 2014
Section: Chapter 2. First Order Equations. Exercises 2.3, page 49
Problem number: 32.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_linear]
\[ \boxed {\left (1+{\mathrm e}^{t}\right ) y^{\prime }+{\mathrm e}^{t} y=t} \] With initial conditions \begin {align*} [y \left (0\right ) = -1] \end {align*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 18
dsolve([(exp(t)+1)*diff(y(t),t)+exp(t)*y(t)=t,y(0) = -1],y(t), singsol=all)
\[ y \left (t \right ) = \frac {t^{2}-4}{2+2 \,{\mathrm e}^{t}} \]
✓ Solution by Mathematica
Time used: 0.071 (sec). Leaf size: 21
DSolve[{(Exp[t]+1)*y'[t]+Exp[t]*y[t]==t,{y[0]==-1}},y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to \frac {t^2-4}{2 \left (e^t+1\right )} \]