2.4 problem 4

Internal problem ID [1652]

Book: Differential equations and their applications, 3rd ed., M. Braun
Section: Section 1.2. Page 9
Problem number: 4.
ODE order: 1.
ODE degree: 1.

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

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

✓ Solution by Maple

Time used: 0.0 (sec). Leaf size: 20

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

\[ y \left (t \right ) = {\mathrm e}^{-t} c_{1} +\frac {{\mathrm e}^{t} \left (2 t -1\right )}{4} \]

✓ Solution by Mathematica

Time used: 0.052 (sec). Leaf size: 26

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

\[ y(t)\to \frac {1}{4} e^t (2 t-1)+c_1 e^{-t} \]