79.1.2 problem 1 (ii)

Internal problem ID [18410]
Book : Elementary Differential Equations. By R.L.E. Schwarzenberger. Chapman and Hall. London. First Edition (1969)
Section : Chapter 3. Solutions of first-order equations. Exercises at page 47
Problem number : 1 (ii)
Date solved : Thursday, March 13, 2025 at 11:55:49 AM
CAS classification : [_quadrature]

\begin{align*} x^{\prime }&=b \,{\mathrm e}^{t} \end{align*}

With initial conditions

\begin{align*} x \left (1\right )&=0 \end{align*}

✓ Maple. Time used: 0.019 (sec). Leaf size: 13

ode:=diff(x(t),t) = b*exp(t); 
ic:=x(1) = 0; 
dsolve([ode,ic],x(t), singsol=all);
 

\[ x = b \left ({\mathrm e}^{t}-{\mathrm e}\right ) \]

✓ Mathematica. Time used: 0.004 (sec). Leaf size: 14

ode=D[x[t],t]==b*Exp[t]; 
ic={x[1]==0}; 
DSolve[{ode,ic},x[t],t,IncludeSingularSolutions->True]
 

\[ x(t)\to b \left (e^t-e\right ) \]

✓ Sympy. Time used: 0.130 (sec). Leaf size: 12

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

\[ x{\left (t \right )} = b e^{t} - e b \]