13.2.4 problem 4

Internal problem ID [2302]
Book : Differential equations and their applications, 3rd ed., M. Braun
Section : Section 1.2. Page 9
Problem number : 4
Date solved : Monday, January 27, 2025 at 05:45:01 AM
CAS classification : [[_linear, `class A`]]

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

✓ Solution by Maple

Time used: 0.001 (sec). Leaf size: 20

dsolve(y(t)+diff(y(t),t) = exp(t)*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: 0.052 (sec). Leaf size: 26

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

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