74.4.71 problem 74 (a)

Internal problem ID [15964]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 2. First Order Equations. Exercises 2.2, page 39
Problem number : 74 (a)
Date solved : Tuesday, January 28, 2025 at 08:24:57 AM
CAS classification : [_separable]

\begin{align*} y^{\prime }&=f \left (t \right ) y \end{align*}

With initial conditions

\begin{align*} y \left (1\right )&=1 \end{align*}

✓ Solution by Maple

Time used: 0.188 (sec). Leaf size: 13

dsolve([diff(y(t),t)=f(t)*y(t),y(1) = 1],y(t), singsol=all)
 

\[ y = {\mathrm e}^{\int _{1}^{t}f \left (\textit {\_z1} \right )d \textit {\_z1}} \]

✓ Solution by Mathematica

Time used: 0.025 (sec). Leaf size: 17

DSolve[{D[y[t],t]==f[t]*y[t],{y[1]==1}},y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to \exp \left (\int _1^tf(K[1])dK[1]\right ) \]