33.4.5 problem Problem 12.13

Internal problem ID [7826]
Book : Schaums Outline Differential Equations, 4th edition. Bronson and Costa. McGraw Hill 2014
Section : Chapter 12. VARIATION OF PARAMETERS. Supplementary Problems. page 109
Problem number : Problem 12.13
Date solved : Tuesday, September 30, 2025 at 05:06:01 PM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} y^{\prime \prime }-7 y^{\prime }&=-3 \end{align*}

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

ode:=diff(diff(y(x),x),x)-7*diff(y(x),x) = -3; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {{\mathrm e}^{7 x} c_1}{7}+\frac {3 x}{7}+c_2 \]

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

ode=D[y[x],{x,2}]-7*D[y[x],x]==-3; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \frac {3 x}{7}+\frac {1}{7} c_1 e^{7 x}+c_2 \end{align*}

✓ Sympy. Time used: 0.083 (sec). Leaf size: 15

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-7*Derivative(y(x), x) + Derivative(y(x), (x, 2)) + 3,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = C_{1} + C_{2} e^{7 x} + \frac {3 x}{7} \]