86.8.7 problem 7

Internal problem ID [23167]
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 5e at page 91
Problem number : 7
Date solved : Thursday, October 02, 2025 at 09:23:42 PM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} y^{\prime \prime }-4 y^{\prime }&=7 \end{align*}

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

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

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

✓ Mathematica. Time used: 0.018 (sec). Leaf size: 24

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

\begin{align*} y(x)&\to -\frac {7 x}{4}+\frac {1}{4} c_1 e^{4 x}+c_2 \end{align*}

✓ Sympy. Time used: 0.086 (sec). Leaf size: 15

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

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