74.5.44 problem 51

Internal problem ID [16008]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 2. First Order Equations. Exercises 2.3, page 49
Problem number : 51
Date solved : Tuesday, January 28, 2025 at 08:26:21 AM
CAS classification : [[_linear, `class A`]]

\begin{align*} y^{\prime }-5 y&=t \end{align*}

✓ Solution by Maple

Time used: 0.001 (sec). Leaf size: 15

dsolve(diff(y(t),t)-5*y(t)=t,y(t), singsol=all)
 

\[ y = -\frac {t}{5}-\frac {1}{25}+c_{1} {\mathrm e}^{5 t} \]

✓ Solution by Mathematica

Time used: 0.057 (sec). Leaf size: 30

DSolve[D[y[t],t]-5*y[t]==t,y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to e^{5 t} \left (\int _1^te^{-5 K[1]} K[1]dK[1]+c_1\right ) \]