73.8.13 problem 13.2 (g)

Internal problem ID [15150]
Book : Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell. second edition. CRC Press. FL, USA. 2020
Section : Chapter 13. Higher order equations: Extending first order concepts. Additional exercises page 259
Problem number : 13.2 (g)
Date solved : Monday, March 31, 2025 at 01:29:22 PM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} y^{\prime \prime }&=2 y^{\prime }-6 \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 16

ode:=diff(diff(y(x),x),x) = 2*diff(y(x),x)-6; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {{\mathrm e}^{2 x} c_1}{2}+3 x +c_2 \]

✓ Mathematica. Time used: 0.015 (sec). Leaf size: 22

ode=D[y[x],{x,2}]==2*D[y[x],x]-6; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to 3 x+\frac {1}{2} c_1 e^{2 x}+c_2 \]

✓ Sympy. Time used: 0.131 (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)) + 6,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = C_{1} + C_{2} e^{2 x} + 3 x \]