Internal problem ID [2028]
Book: Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath.
Boston. 1964
Section: Exercise 11, page 45
Problem number: 18.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_1st_order, _with_linear_symmetries], _Bernoulli]
\[ \boxed {y^{\prime }+y-y^{2} {\mathrm e}^{-t}=0} \] With initial conditions \begin {align*} [y \left (0\right ) = 2] \end {align*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 8
dsolve([diff(y(t),t)+y(t)=y(t)^2*exp(-t),y(0) = 2],y(t), singsol=all)
\[ y \left (t \right ) = 2 \,{\mathrm e}^{t} \]
✓ Solution by Mathematica
Time used: 0.281 (sec). Leaf size: 10
DSolve[{y'[t]+y[t]==y[t]^2*Exp[-t],{y[0]==2}},y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to 2 e^t \]