67.3.22 problem 4.6 (b)

Internal problem ID [16343]
Book : Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell. second edition. CRC Press. FL, USA. 2020
Section : Chapter 4. SEPARABLE FIRST ORDER EQUATIONS. Additional exercises. page 90
Problem number : 4.6 (b)
Date solved : Thursday, October 02, 2025 at 01:21:13 PM
CAS classification : [_quadrature]

\begin{align*} y^{\prime }-4 y&=2 \end{align*}

✓ Maple. Time used: 0.001 (sec). Leaf size: 12

ode:=diff(y(x),x)-4*y(x) = 2; 
dsolve(ode,y(x), singsol=all);
 

\[ y = -\frac {1}{2}+{\mathrm e}^{4 x} c_1 \]

✓ Mathematica. Time used: 0.017 (sec). Leaf size: 24

ode=D[y[x],x]-4*y[x]==2; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to -\frac {1}{2}+c_1 e^{4 x}\\ y(x)&\to -\frac {1}{2} \end{align*}

✓ Sympy. Time used: 0.067 (sec). Leaf size: 12

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-4*y(x) + Derivative(y(x), x) - 2,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = C_{1} e^{4 x} - \frac {1}{2} \]