78.9.8 problem 5 (b)

Internal problem ID [18177]
Book : DIFFERENTIAL EQUATIONS WITH APPLICATIONS AND HISTORICAL NOTES by George F. Simmons. 3rd edition. 2017. CRC press, Boca Raton FL.
Section : Chapter 3. Second order linear equations. Section 14. Introduction. Problems at page 112
Problem number : 5 (b)
Date solved : Thursday, March 13, 2025 at 11:48:18 AM
CAS classification : [[_2nd_order, _missing_x]]

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

✓ Maple. Time used: 0.001 (sec). Leaf size: 16

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

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

✓ Mathematica. Time used: 0.011 (sec). Leaf size: 22

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

\[ y(x)\to -2 x+\frac {1}{2} c_1 e^{2 x}+c_2 \]

✓ Sympy. Time used: 0.129 (sec). Leaf size: 14

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

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