68.4.71 problem 74 (a)

Internal problem ID [17251]
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 : Thursday, October 02, 2025 at 01:59:55 PM
CAS classification : [_separable]

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

With initial conditions

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

✓ Maple. Time used: 0.043 (sec). Leaf size: 13

ode:=diff(y(t),t) = f(t)*y(t); 
ic:=[y(1) = 1]; 
dsolve([ode,op(ic)],y(t), singsol=all);
 

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

✓ Mathematica. Time used: 0.019 (sec). Leaf size: 17

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

\begin{align*} y(t)&\to \exp \left (\int _1^tf(K[1])dK[1]\right ) \end{align*}

✓ Sympy. Time used: 0.183 (sec). Leaf size: 15

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(-f(t)*y(t) + Derivative(y(t), t),0) 
ics = {y(1): 1} 
dsolve(ode,func=y(t),ics=ics)
 

\[ y{\left (t \right )} = \left (e^{\int f{\left (t \right )}\, dt}\right ) e^{- \int \limits ^{1} f{\left (t \right )}\, dt} \]