14.1.4 problem 4

Internal problem ID [2475]
Book : Differential equations and their applications, 4th ed., M. Braun
Section : Chapter 1. First order differential equations. Section 1.2. Linear equations. Excercises page 9
Problem number : 4
Date solved : Monday, January 27, 2025 at 05:53:40 AM
CAS classification : [[_linear, `class A`]]

\begin{align*} y^{\prime }+y&={\mathrm e}^{t} t \end{align*}

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 20

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

\[ y = {\mathrm e}^{-t} c_1 +\frac {{\mathrm e}^{t} \left (2 t -1\right )}{4} \]

✓ Solution by Mathematica

Time used: 0.053 (sec). Leaf size: 26

DSolve[D[y[t],t]+y[t]==t*Exp[t],y[t],t,IncludeSingularSolutions -> True]
 

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