68.2.8 problem 13

Internal problem ID [17136]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 1. Introduction to Differential Equations. Review exercises, page 23
Problem number : 13
Date solved : Thursday, October 02, 2025 at 01:44:15 PM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} 12 y-7 y^{\prime }+y^{\prime \prime }&=2 \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 18

ode:=diff(diff(y(x),x),x)-7*diff(y(x),x)+12*y(x) = 2; 
dsolve(ode,y(x), singsol=all);
 

\[ y = {\mathrm e}^{4 x} c_2 +{\mathrm e}^{3 x} c_1 +\frac {1}{6} \]

✓ Mathematica. Time used: 0.009 (sec). Leaf size: 25

ode=D[y[x],{x,2}]-7*D[y[x],x]+12*y[x]==2; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to c_1 e^{3 x}+c_2 e^{4 x}+\frac {1}{6} \end{align*}

✓ Sympy. Time used: 0.095 (sec). Leaf size: 19

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(12*y(x) - 7*Derivative(y(x), x) + Derivative(y(x), (x, 2)) - 2,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = C_{1} e^{3 x} + C_{2} e^{4 x} + \frac {1}{6} \]