1.3 problem 3

Internal problem ID [450]

Book: Elementary differential equations and boundary value problems, 10th ed., Boyce and DiPrima
Section: Section 2.1. Page 40
Problem number: 3.
ODE order: 1.
ODE degree: 1.

CAS Maple gives this as type [[_linear, `class A`]]

\[ \boxed {y+y^{\prime }=1+t \,{\mathrm e}^{-t}} \]

Solution by Maple

Time used: 0.0 (sec). Leaf size: 18

dsolve(y(t)+diff(y(t),t) = 1+t/exp(t),y(t), singsol=all)
 

\[ y \left (t \right ) = \left (\frac {t^{2}}{2}+{\mathrm e}^{t}+c_{1} \right ) {\mathrm e}^{-t} \]

Solution by Mathematica

Time used: 0.052 (sec). Leaf size: 27

DSolve[y[t]+y'[t] == 1+t/Exp[t],y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to \frac {1}{2} e^{-t} \left (t^2+2 e^t+2 c_1\right ) \]