86.7.5 problem 5

Internal problem ID [23152]
Book : An introduction to Differential Equations. By Howard Frederick Cleaves. 1969. Oliver and Boyd publisher. ISBN 0050015044
Section : Chapter 5. Linear equations of the second order with constant coefficients. Exercise 5c at page 83
Problem number : 5
Date solved : Thursday, October 02, 2025 at 09:23:32 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} x^{\prime \prime }-6 x^{\prime }-7 x&=4 z -7 \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 21

ode:=diff(diff(x(z),z),z)-6*diff(x(z),z)-7*x(z) = 4*z-7; 
dsolve(ode,x(z), singsol=all);
 

\[ x = {\mathrm e}^{-z} c_2 +{\mathrm e}^{7 z} c_1 -\frac {4 z}{7}+\frac {73}{49} \]

✓ Mathematica. Time used: 0.011 (sec). Leaf size: 30

ode=D[x[z],{z,2}]-6*D[x[z],z]-7*x[z]==4*z-7; 
ic={}; 
DSolve[{ode,ic},x[z],z,IncludeSingularSolutions->True]
 

\begin{align*} x(z)&\to -\frac {4 z}{7}+c_1 e^{-z}+c_2 e^{7 z}+\frac {73}{49} \end{align*}

✓ Sympy. Time used: 0.114 (sec). Leaf size: 22

from sympy import * 
z = symbols("z") 
x = Function("x") 
ode = Eq(-4*z - 7*x(z) - 6*Derivative(x(z), z) + Derivative(x(z), (z, 2)) + 7,0) 
ics = {} 
dsolve(ode,func=x(z),ics=ics)
 

\[ x{\left (z \right )} = C_{1} e^{- z} + C_{2} e^{7 z} - \frac {4 z}{7} + \frac {73}{49} \]