67.4.21 problem 5.3 (a)

Internal problem ID [16390]
Book : Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell. second edition. CRC Press. FL, USA. 2020
Section : Chapter 5. LINEAR FIRST ORDER EQUATIONS. Additional exercises. page 103
Problem number : 5.3 (a)
Date solved : Thursday, October 02, 2025 at 01:27:30 PM
CAS classification : [_quadrature]

\begin{align*} y^{\prime }-3 y&=6 \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=5 \\ \end{align*}

✓ Maple. Time used: 0.023 (sec). Leaf size: 12

ode:=diff(y(x),x)-3*y(x) = 6; 
ic:=[y(0) = 5]; 
dsolve([ode,op(ic)],y(x), singsol=all);
 

\[ y = -2+7 \,{\mathrm e}^{3 x} \]

✓ Mathematica. Time used: 0.017 (sec). Leaf size: 14

ode=D[y[x],x]-3*y[x]==6; 
ic={y[0]==5}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to 7 e^{3 x}-2 \end{align*}

✓ Sympy. Time used: 0.071 (sec). Leaf size: 10

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-3*y(x) + Derivative(y(x), x) - 6,0) 
ics = {y(0): 5} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = 7 e^{3 x} - 2 \]